Helicopters will be used to track down the three-year-old animal, which may be put down as a result of his repeated breakouts from Karoo National Park in the south of the country.
"He is clearly a troublesome lion and could be a danger to humans," South African National Parks spokesman Reynold Thakhuli told AFP.
"Authorities will have to consider various management methods to ensure his safety and that of people. Such interventions might include euthanizing the animal."
He has already killed a cow.
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During his last escape, he roamed 300 kilometres from the park, killing 30 animals over three weeks before being shot by a tranquiliser dart fired from a helicopter.
At the time, wildlife officials said he had been forced out of the park by older lions.
"This time we don't know what might have driven him away. It could be that he became used to easy prey while outside the park," said Thakhuli.
The last wild lion in the area was shot in 1842.