Fox said an anti-poaching dog alerted her handler to noises coming from the lion enclosure early Monday morning, but the remains were not found until the next afternoon.
The lions can be noisy at night and so the handler did not check on the enclosure that night, Fox posted.
The human remains were discovered by a field guide the next afternoon.
It is unclear how many poachers entered the enclosure, but officials said they believe at least three people were involved.
Officials said the enclosure holds a pride of six lions.
"They strayed into a pride of lions. It's a big pride so they didn't have too much time," Fox told AFP news agency. "We're not sure how many there were -- there's not much left of them."
Fox said several of the lions had to be tranquilized before the remains could be removed from the area.
There has been a rise in rhino poaching across the African continent in recent years, according to the BBC.
Rhino horns are believed to have aphrodisiac qualities in parts of Asia.
Nine rhinos have been killed in the Eastern Cape province this year alone.
More than 7,000 rhinos have been killed across South Africa in the last decade.