The bodies were found Tuesday afternoon after one of the reserve's field guides alerted their Anti-Poaching Unit.
The horns are prized for their medicinal value and used in traditional Chinese medicines, though there is no science to back up their touted "cure-all" powers.
He added that they suspect there were three people killed because they found "three sets of shoes and three sets of gloves".
Police spokesperson Captain Mali Govender said: "A riffle and an axe were found at the scene".
Africa is seeing a growth of rhino poachers to keep up with demand for rhino horn in parts of China and Vietnam. Currently, Fox said, it's not certain how many poachers were killed. Staff members heard a commotion coming from the area where lions are kept and, suspecting that the lions' activity had disturbed the dog, did not immediately investigate further.
When the anti-poaching team arrived, they had to tranquilise the pack of lions before they could get near the remains, where they found a silenced hunting rifle and a large axe. The Washington Post was unable to reach Fox for comment.
The 30 square mile park is home to all of Africa's "Big Five" - rhinos, lions, elephants, buffalos, and leopards. Still, in 2017 alone, more than 1,000 adult rhinos were slaughtered.
This is not the first time that poachers have targeted the Eastern Cape.
Rhinos have had a rough go in the Sibuya province lately.
"It was a bit of luck for us and not so much luck for them", he said.
"It's not a crime of poverty", she said.
"They came heavily armed with hunting rifles and axes which we have recovered and enough food to last them for several days so we suspect they were after all of our rhinos here", Fox said.