It is believed to have left the park, near the small town of Beaufort West, through a hole under the fence.
"A helicopter is on standby and rangers are walking around with attacker dogs in case they came across the lion," South African National Parks official Fayrouch Ludick told the BBC.
A  tourist was killed last week by a lion at a game park near Johannesburg.
African news updates
The American woman was mauled after the lion jumped through a car window which was open in breach of park rules.
Ms Ludick said park officials were confident that the three-year-old male lion, which escaped from the Karoo National Park, would be recaptured.
"The spoor has been found by the trackers, but it's just a matter of keeping up with it through the mountains and ravines," she said, South Africa's Eyewitness News reports.
The Karoo National Park is in a sparsely populated area surrounded mainly by farms.
Ms Ludick warned people not to approach the lion if they saw it.
"Can't really judge the temperament of the lion because it is wild and it stays in a national park of under 90,000 hectares of land. It is not tame and has no exposure to humans often so there is no telling what it can do if it does come into contact with a human," Ms Ludick told the BBC.
News of the lion's escape is spreading on local social media under #missinglion.
The lion was believed to have escaped on Friday, and a farmer who spotted lion tracks on his farm alerted park officials, South Africa's News24 website reports.
Park officials believe a hole formed under the fence after a heavy flow of water, making it possible for the lion to escape, it reports.

Tom Lucking found a gold pendant inlaid with a profusion of garnets while metal detecting on farmland in 2014.
The 7cm (2.8in) item was found in the grave of a female and has been described as one of the "most elaborate...ever found".
It was declared treasure alongside other items at an inquest in Norwich.
Why is Norfolk a treasure hunting hotspot?
Mr Lucking, 23, a student from Felixstowe who is in his final year studying history at the University of East Anglia, said the discovery "had certainly given me a good dissertation project".
He said: "It makes me pleased I've put time and effort in metal detecting in that field and it was worth going out into the cold and rain over the years to find those things."
He unearthed the pendant whilst exploring a field near Diss, after initially detecting a bronze bowl.
After the inquest on Monday, Mr Lucking said: "You can hope, but never really expect to find something like this.
"It's not about the money value, it's about finding something that makes you re-think the whole history of an area."
Julie Shoemark, finds officer for Norfolk, said the burial dates to the cusp of the early Christianisation of Anglo-Saxon England, around the middle of the 7th century AD.
She said: "Within a century of this lady's death, burial practices had completely changed and people were being interred with no associated grave goods, as seen in the burials from Great Ryburgh.
"She was undoubtedly a lady of some status in the community of East Anglia as the magnificent garnet inlaid pendant and associated grave goods demonstrate."
Dr Andrew Rogerson, of the county's Heritage Environment Services, previously described the pendant as one of the "most elaborate...ever found".
He said: "It would seem we have something of major significance."
The British Museum report for the coroner listed a number of precious coins and jewellery found alongside the woman's skeleton.
British Museum identification of items
Mr Lucking has been metal detecting since he was 11-years-old.
He said he will share proceeds from the sale with the owner of the land and his friend, Stuart Isaacs, who treasure hunts with him.
Norwich Castle Museum is understood to be interested in buying the pendant after it is formally valued by the British Museum.
Game rangers are searching for a lion which escaped from a wildlife park in South Africa's Western Cape province.
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A student who found Anglo Saxon jewellery of "national significance" said the discovery has made three years exploring the field worthwhile.