The cheetahs at the Kragga Kramma Game Reserve in Port Elizabeth had been raised by keepers and were supposed to be tame enough to allow visitors to pose for pictures and pet them, The Daily Telegraph reported.
Violet D'Mello, 60, of Aberdeen, said one of the cheetahs first clawed a 7-year-old girl. She said she was attacked when she tried to stop the girl's brother from running around.
"They weren't vicious. You could tell they were just excited, but it became serious very quickly," she told The Times of South Africa.
She said the cheetahs, brothers from the same litter, had her on the ground.
"You have to understand, these are big animals," D'Mello said. "Something inside me just said, 'Don't move. Don't move at all -- don't react, just play dead."
Graham Kerley of the Center for African Conservation Ecology said cheetahs are not "tame pussycats."
"The bottom line is, cheetahs are wild animals, and adult cheetahs have the capacity to hurt very badly," he said.
Mike Cantor, the manager of the reserve, said no decision has been made on whether the cheetahs should continue to interact with the public, but he said they will not be killed.
2014: The Year in Music [PHOTOS]