After a farmer reported that he'd found lion tracks on his land, the park's trackers, who belong to the indigenous San group, began following the tracks with the farmer, South African National Parks said in a statement.
A helicopter being used for a wildlife census also joined the search. The carcass of a gemsbok, a large antelope, was placed to lure the lion but it didn't appear.
The 3-year-old male lion apparently left Karoo National Park on Friday through a rain-eroded hole under a fence and disappeared into "terrain (that) is mountainous, with many river valleys, thus making tracking difficult," the park service said.
"The lion is covering vast areas," van den Heever said. Tracks were seen 21 kilometers from the park.
One tracking dog named Bullet is also being used, a park official said.
The area, in the Karoo semi-desert, is sparsely populated. Beaufort West, on the park's edge, has some 34,000 inhabitants.
"Members of the public who may see the lion or any signs of it are requested not to confront it and to contact" a parks official, the SANP statement said.
While lion escapes are rare in South Africa, in Kenya the growing human population is settling in areas used by the lions' prey, said Paul Udoto, a spokesman for the Kenya Wildlife Service.
Kenya Wildlife Service Deputy Director and Head of Species Patrick Omondi said that because Kenya has an open park system, the lions follow their prey to areas where people have settled, killing livestock and sometimes people.