Q:

How were knee injuries treated in Ancient Greece?

Today knee injuries, for example ACL tears*, are a pretty common injury, especially with fighters (Judo, Wrestling, BJJ, MMA, …). Since the Greeks practiced a lot of wrestling and pankration, knee injuries must have been a common thing, right? Besides the athletic stuff, soldiers on the battlefield surely had to deal with a similar amount of knee injuries (while training or on the battlefield itself).
To what extend could they treat knee injuries (of any kind) back then?
What were their methods? Did they try some sort of knee surgery?
Are there any scripts or depictions of how common such injuries would occur with athletes/soldiers?
*There are four primary ligaments in your knee, two of them form an X in the center of the knee. If those tear, e.g. through a wrong twist or a sudden stop motion, that woud be called an ACL tear. There are various degrees of tear I think and also similar injuries when other ligaments get torn. (disclaimer: I am not a medic)
See: 
Anterior Cruciate Ligament (ACL) Injuries (American Academy of Orthopaedic Surgeons)
Wikipedia: Anterior cruciate ligament injury

A:

The most common injuries to the knee are occurring in the bones, muscles, cartilage, meniscus, ligaments and tendons. These have to be considered for antiquity between being known, identified and correctly explained and treated.
For fractures and dislocations treatments after the hellenistic era were already very similar to the best attempts that can be made today.  Muscle, skin and even blood vessel injuries could also be treated with quite advanced techniques and even surgical interventions. The other types of injuries would have to be seen as not having an overly bright prognosis if they really required the attention of a medicus. 
The ligaments were already known to Hippokrates. Even before him the Eygptian "Smith papyrus" describes these structures. The amount of anatomical knowledge was quite impressive, especially related to bones and joints:

Hippocrates (5th–4th century B.C.), the founder of scientific medicine, left a valuable heritage of knowledge and methodology, which extends to almost all branches of modern medicine. Among the many fields of medicine he explored, he devoted much of his scientific interest to the study of orthopedics. In fact, some of the principles found in the Hippocratic treatises On Fractures and On Joints are still valid today. This great physician also was the first to deal with the anatomy and the pathology of human spine. In his books, he provides a precise description of the segments and the normal curves of the spine, the structure of the vertebrae, the tendons attached to them, the blood supply to the spine, and even its anatomic relations to adjacent vessels. The Hippocratic list of spinal diseases includes tuberculous spondylitis, post-traumatic kyphosis, scoliosis, concussion, dislocations of the vertebrae, and fractures of the spinous processes. Hippocrates devised two apparatuses, known as the Hippocratic ladder and the Hippocratic board, to reduce displaced vertebrae. Those pioneer methods are deemed to be the precursors to the sophisticated techniques used in spine surgery today. Because of his thorough study of spinal diseases and their management, which was the first such study in orthopedics in the history of medicine, Hippocrates should be regarded as the father of spine surgery.
Spyros G Marketos: "Hippocrates: The Father of Spine Surgery", Spine: July 1, 1999 - Volume 24 - Issue 13 - p 1381.

What was missing at the time was a correct understanding of the precise function of these ligaments:

The anterior cruciate ligament (ACL) has entertained scientific minds since the Weber brothers provided biomechanical insight into the importance of the ACL in maintaining normal knee kinematics. Robert Adams described the first clinical case of ACL rupture in 1837 some 175 years to date, followed by Mayo-Robson of Leeds who performed the first ACL repair in 1895. At that time, most patients presented late and clinicians started to appreciate signs and symptoms and disabilities associated with such injuries. Hey Groves of Bristol provided the initial description of an ACL reconstruction with autologous tissue graft in 1917, almost as we know it today.
Oliver Schindler: "Surgery for anterior cruciate ligament deficiency: a historical perspective", Knee Surgery, Sports Traumatology, Arthroscopy, January 2012, Volume 20, Issue 1, pp 5–47. 

That means that most of the time, for this specific injury, the Greeks would have to recurse to hope for self-healing, which may not always be the case. Stiffened knees were no uncommon sight.
The first glimpse of understanding the correct function of the ligaments came when Galen discarded the assumption that they were part of the nervous system.

The cruciate ligaments have been known about since old Egyptian times and their anatomy was described in the famous Smith Papyrus (3000 BC). Hippocrates also (460–370 BC) mentioned the subluxation of the knee joint with ligament pathology, but Claudius Galen, a Greek physician in the Roman Empire, was the first to describe the true nature of the ACL.
Prior to Galen’s description, it was believed that the cruciate ligaments were part of the nervous system, but Galen was the first to describe the ACL as being a structure that supports the joint and prevents abnormal knee motion. He called the cruciate ligaments genu cruciata but he did not describe in detail their function.
In 1836, the Weber brothers from Goettingen in Germany noted an abnormal anterior-posterior movement of the tibia after transection of the ACL. They also described the roll and glide mechanism of the knee and the tension pattern of the different bundles of the cruciate ligaments and, to our knowledge, were the first to describe that each bundle of the ACL was tensioned in different degrees of flexion of the knee joint.
Nikolaos Davarinos et al.: "A Brief History of Anterior Cruciate Ligament Reconstruction", Advances in Orthopedic Surgery, Volume 2014, Article ID 706042,

On an again more general perspective of how the Greeks would have treated sports injuries, or battle field injuries for that matter: Herodicus is called the "father of sports medicine". (Modern doctors love this concept, however ahistorical it is.) This man has indeed made some important contributions to the field. But as Hippokrates and Galen, he was subscribed to the theory of humoral pathology, the science of the juices (or bodily fluids). His theoretical framework was like this:

   Eventually Herodicus invented his own medical system, which first of all included a strict diet, consisted of grains and other foods generally regarded as unappetizing. His medical theory embodied also exhaustive training as a treatment method.

Thus emphasising physiotherapy and diet, despite that he is now known primarily for his advice on massages. But strictly following his advice might not always have been the best idea:

However, Herodicus sometimes followed this line of thinking to extremes and his instructions for a healthy life were quite complex. Thus, some ancient authors criticised him for being obsessive with his treatments. For example, the writer of Epidemics (: 6.3.18) notes that ‘‘Herodicus have killed fever patients by running exercises, many bouts of wrestling and vapour baths.’’ Platon in Res Publica (: 406.a.4–b.8) criticizes also his method to mix gymnastic training with medicine. It seems that the same opinion was shared by Aristotle in Rhetorica (: 1361b 4–6): ‘‘many men are in good health, for example Herodicus, but no one would congratulate them on their health, because they abstain from all or most human pleasures.’’ However, Herodicus persistency may be what separated him from others.
Anastasios D. Georgoulis et al.: "Herodicus, the father of sports medicine", Knee Surg Sports Traumatol Arthrosc (2007) 15:315–318.

Apart from the usual approaches – blood letting, diet, exercise, rest – there were of course more magical methods: praying, offerings to the gods or sleeping near a temple. But some examples for real, rational and physical treatments are found in numerous books. The knife, the lance, the needle were all available tools to get to the matter:

 
From Lawrence J. Bliquez: "The Tools of Asclepius. Surgical Instruments in Greek and Roman Times", Brill: Leiden, Boston, 2014.

Straps, bandages, crutches, cups for cupping were employed, some physical stretch banks described by Hippokrates. Whereas at roughly the same time the rustic Romans seem to have thought that if there is something, anything wrong, just put some cabbage on it.
We sadly do not know what women healers, most farming related traditions or those used by unprominent traveling healers would do in such a knee injury, as they surely did but were apparently not deemed worthy enough to be recorded or transmitted through time. That means from this fact alone that a huge part of all the knowledge never made it into writing in the first place.
But from the corpus Hippokraticum, from Celsus or Galen, to name just a few of the most prominent of the famous doctors, we might assess the state of what was considered the art.
We might compare an ancient treatise on treatment for comparison with modern methods; to quote from Celsus,  who wrote the first substantial treatment of surgery after Hippocrates and the most extensive in classical Antiquity. He was a philosopher – or encyclopaedist – more than a medicus himself:

Since I have described the above, I can be held also to have described displacements in the legs: for in this kind of accident also there is some similarity between the thigh and upper arm, between the tibia and ulna, between the foot and the hand.   But there are also some special points to note about the legs.
  The thigh-bone may be moved out of place in all four directions, oftenest inwards, next outwards, very rarely forwards or backwards. If it has been dislocated inwards, the leg is longer than the other, and is bowed; for the point of the foot looks outwards if outwards, the leg becomes shorter and knock-kneed, and the foot is inclined inwards; the heel in walking does not touch the ground, but only the extreme end of the sole ; the leg in this case supports the rest of the body better and more uprightly than in the other and there is less need for a stick. If forwards, the leg is extended and cannot be bent; as far as the heel the injured leg is the length of the other one, but the extremity of the sole is less bent forward and in this case there is marked pain, and very often the urine is suppressed. When the inflammation and pain have subsided, the patients walk fairly and the whole of their foot touches the ground. If backwards, the leg cannot be stretched out, and is shorter; when the patient is standing the heel in these cases too cannot touch the ground. But the great danger with regard to the thigh is that it is difficult to replace, or, after replacement, slips again out of position. Some hold that it always does so; but such renowned authorities as Hippocrates' and Diodes and Phylotimus and Nileus and Heraclides of Tarentum have related that they had completely restored such cases; nor would Hippocrates, Andreas, Nileus, Nymphodorus, Protarchus, Heraclides, and a certain smith as well, have invented so many sorts of instruments for making extension on the thigh after this accident, if it had all been of no use. But although that opinion is a false one, there is this truth in it: since the ligaments and muscles there are very strong, if they retain their strength they scarcely allow of replacement; if not, they do not keep in place afterwards. Replacement, then, is to be attempted; and if the limb is weak it is sufficient to stretch it by straps, one from the groin, extension on the thigh after this accident, if it had all been of no use.
  another from the knee ; if stronger, the assistants will have more purchase if they have knotted the straps around strong poles ; and if after pressing the lower ends of the poles against firm supports, they have drawn the upper ends towards themselves with both hands. Even more forcible pressure can be exerted by stretching the limb over a bench," at either end of which is a windlass to which the straps are attached; when these are rotated as in a winepress, it is possible, by continuing to do this, even to rupture the ligaments and muscles, and not merely to stretch them. Now the patient is to be laid upon this bench, on his face or back or side, so that that part is always the higher into which the bone has slipped, and that from which it has receded the lower. When the sinews have been stretched, if the bone comes forwards, some round object is placed over the groin and the patient's knee must be pulled back over it with a jerk, in the same way and for the same reason for which this was done in the case of the forearm  as soon as the thigh can be bent up, the bone is in place. In the other cases, when the bones under extension have receded a little from each other, the surgeon should force the projecting part back, whilst an assistant presses the hip in the opposite direction. When the bone is replaced nothing further need be done, but the patient must be kept in bed for a rather long time or the thigh may become displaced again on moving while the sinews are still
  relaxed.   
It is very well known that the knee'' is put out externally and internally and backwards. Many have written that it does not slip out forwards ; and this may be very near the truth, for the knee-cap is there right in front and holds the head of the tibia in place. Meges, however, has recorded a case in which he replaced a knee which had slipped forwards." In cases affecting the knee-joint the sinews can be extended by the same means as I have described for the thigh. And when it has slipped out backwards, as described above, a round ball of some kind is placed on the ham, and when the leg is bent up over it, the knee slips back again. In the other cases it is to be replaced by the surgeon's hands while the bones are being drawn apart in opposite directions.
Celsus Book VIII. 21. 1-23. Quoted from Celsus: "De Medicina", with an English translation by W. G. Spencer Ms. Lond., F.B.C.S. Eno.
  In Three Volumes, III, Loeb Classical Library, Heinemann, Harvard University Press, 1961, p579ff.

We can be sure that the Greeks and Romans have tried some surgery on knees. But they admitted in their texts – readily apparent in hippokratic texts – that any such procedure was very unlikely to be successful, thereby more outlining a desire or programme than documenting established knowledge. Tears might heal to usefulness on their own, ruptures not so well – and when cartilage is gone, it is really gone.  Symptomatic relief was possible through a range of options, full recovery to pre-injury state more or less seldom.
Cutting into the patients should be avoided in many traditions, not in the least because of the risk of infection; while other traditions insisted that a real doctor was only one who wielded the knife profusely.

Celsus divided his subject into dietetics, pharmacy, and surgery; thus the two books on surgery (7 and 8) stand out prominently. He further divides surgery into (1) cases where the practitioner himself must make a wound (e.g. lancing an abscess or removing a nasal polyp), or where a pre-existing wound can be better treated by the hand than by medicines (e.g. removing an embedded missile) (book 7), and (2) cases involving broken or dislocated bones (book 8). In book 5, however, under the rubric ‘medications’, Celsus deals with topical treatments for wounds, ulcers, and similar conditions. Thus, what defines surgery is manual action, not the problem addressed, or the status of the practitioner.[…]
  Celsus’ showcasing of ‘the work of the hand’ essentially created surgery as a coherent category of medical thinking, populated by a wide-ranging repertoire of operations as well as treatments for trauma. The implication is that a ‘surgeon’ should be master of both. Moreover, on one significant occasion, Celsus refers to the practitioner as chirurgicus, namely when describing the psychological and physical requirements of wielding the knife (7, Proem. 4).

This collection from Celsus' works marks the absolute highpoint of surgery knowledge in antiquity, as Galen's surviving works abstain from mentioning surgery as much as the corpus hippocraticum:

The procedures described are not particularly invasive, and are confined to wound surgery. Indeed, wound surgery marks the boundary between the Hippocratic iatros and the people whom The Oath calls ergatai andres —‘men who work’—at the surgical removal of bladder stones. As the Hippocratic Oath implies, the ergatai andres were specialist experts in this complex operation—a procedure which required particular equipment, trained assistants, and constant, focused practice that would not be available to the generalist doctor. Hence the Hippocratic iatros of the treatises wielded ‘the knife’ (síderos—literally, ‘an iron [tool]’) that exposes cranial fractures, or cut away mangled  flesh around a wound, but eschewed ‘the knife’ that opens the body. The well-known passage in Aphorisms 7.87—‘What drugs will not cure, the knife will; what the knife will not cure, the cautery will; what the cautery will not cure must be considered incurable’—implies a problem like gangrene or sepsis, treated  first with caustics, then ablation, and if all else fails, cautery. This inflection of ‘the knife’ orients us to the modest horizon of Hippocratic surgery.  
Faith Wallis: "Pre-modern Surgery: Wounds, Words, and the Paradox of ‘Tradition’", section "Antiquity: ‘surgery’ without ‘surgeons’", in: Thomas Schlich (Ed): "The Palgrave Handbook of the History of Surgery", Palgrave MacMillan: London, 2018, p52–56.

Lifted from my own comment:
All the above means that knee injuries were not necessarily "as common as they are now". But that was foremost because of a more robust physis due to a more natural upbringing back then. People were sitting much less, had no cars, etc. And above all: they did not use sport/running shoes! That might be surprising, but modern shoes make things worse and cause more injury in that regard. The cushioning and stabilisation makes ligaments and muscles weaker over time, prevent their proper development from childhood and promote the wrong runnig style: heel striking increases the physical impact forces transmitted to the knees. If we look at the rate of injury in the knee for Tarahumara or Kenian barefoot runners we see much less of those.
Then the self-healing aspect: not always career ending. But in severe cases: yeah, pretty much extremely tough luck for the athlete where now on operation might help. Many cases of modern surgery on the knee are either not really necessary or as bad in their outcomes as you would expect if you were brought on a stretcher from the games to a battle hardened surgeon that was used to extract missiles and amputate limbs in a row.
For soldiers, restraint in physical exercise may not have been an option at all, but while sport was held in high regard by the Greeks and Romans, they knew of the dangers involved in overdoing it.

Galen, and all doctors after Galen, thus advocated proper diet. Galen recommended a diet designed to thin the humours, consisting of fish, fowl, barley, beans, onions, and garlic for all chronic diseases. They recommended sensible exercise. Galen abhorred gymnastics as too violent––the claim that gymnastics was the science of health and medicine the science of disease seemed to him to take no account of sports injuries––but recommended instead ‘exercise with the small ball’, a game of catch. They recommended the regular use of laxatives and prophylactic bloodletting. But they also recommended control of the passions, particularly anger.
David Wootton: "Bad Medicine. Doctors Doing Harm Since Hippocrates", Oxford University Press: Oxford, New York, 2006, p 39.

