Striker Nelson, 19, went off injured just minutes after being introduced as a substitute in Saturday's 1-1 draw with Plymouth Argyle.
He has played four games for Pools since joining in January.
"It's doubtful that he will be able to play again this season," head physio Ian Gallagher told the club website.
Manager Dave Jones said: "It's so unfortunate for Andrew and for us.
"He's come here looking to gain some senior experience, had done well in the games he's played and has slotted in well with the rest of the lads."

And this year the yacht received a record score of 96%, the highest mark ever awarded to a visitor attraction in Scotland.
It was rated by national tourism organisation VisitScotland.
VisitScotland's quality assurance scheme, is the official measure of quality for tourism businesses.
Tourism businesses are assessed on the welcome, attitude, knowledge and efficiency of staff, as well as audience level, interpretation, maintenance and cleanliness.
With 308,906 visitors in 2015, the Royal Yacht last week announced 2015 as its best since its opening year in 1999.
Almost five million people from around the world have visited The Queen's former yacht since it opened to visitors in Edinburgh in 1998.
Britannia's chief executive Bob Downie said: "To be the best in Scotland once is a fantastic achievement, but to do this for 10 consecutive years is a phenomenal tribute to our staff who go the extra mile to ensure that all our visitors have a great experience when they visit Britannia.
"The true test of any great organisation is consistency of performance, delivering great value for time and money, year in year out, and there is no doubt that our pioneering approach to providing great customer experiences has underpinned our success."
Malcolm Roughead, VisitScotland's chief executive, said: "I'd like to congratulate Britannia on this fantastic achievement, which demonstrates an outstanding commitment to quality and excellence in every aspect of the business.
"Retaining the accolade of Scotland's best attraction for 10 years running, Britannia is setting the standards for tourism in Scotland, and it is a real testament to the total commitment shown by their staff to consistently deliver a world-leading customer experience."

Cleveland Police have also confirmed a 26-year-old man has been arrested on suspicion of child abduction, following the girl's disappearance on Thursday.
The girl from Teesside was found earlier, after being reported missing at 22:00 BST.
The search for her involved 30 officers.

An altercation broke out between two men inside a fast food outlet about 00:35 BST on Sunday which then continued outside.
Police said the suspect is described being aged in his early 20s, of slim to medium build, with cropped dark hair shaved on both sides.
Police have appealed for information.
Hartlepool United loanee Andrew Nelson has returned to parent club Sunderland for treatment after scans showed he has damaged medial knee ligaments.
[NEXT_CONCEPT]
The Royal Yacht Britannia has been judged as Scotland's best visitor attraction every year for the past decade.
[NEXT_CONCEPT]
A missing girl believed to have left home to see a man she met online has been found, say police.
[NEXT_CONCEPT]
A man in his 30s is in a serious condition in hospital after suffering a head injury during an assault in Belfast city centre.