The warrant officer was attacked while trying to photograph the pair of collared captive-bred cheetahs, a colleague who declined to be identified told AFP.
"The lady was trying to take a picture and then she got injured, but... It's not a serious injury," she told AFP.
The incident occurred on Tuesday at Makhado Air Force Base in the northeast near the border with Zimbabwe, the force said in a statement.
Cheetahs, the world's fastest land animals, are used as "a sustainable means of controlling wildlife populations that pose a hazard to aviation safety," the statement added.
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The Hoedspruit Endangered Species Centre, an animal charity, said on its website that it had recently donated two cheetahs, Tobie, six, and Wim, seven, to the Makhado base.
But officials were unable to confirm if the pair had been identified as those involved in the attack.
The military described the attacks as "unprecedented" and started an investigation.