The three male animals were killed in Tzaneen Lion and Predator Park in northern Limpopo province on Wednesday, police spokesman Moatshe Ngoepe said on Friday.
It is not known how the killers got through the security system surrounding the private game park, Ngoepe said.
DPA was unable to contact park owner Andre de Lange, who media reports quoted as saying that the killings may have been an inside job.
After entering the park, the killers cut the fence of the lion cage, Ngoepe said.
He declined to confirm reports that the lions had been poisoned, because the investigation is still ongoing.
Reports said the lion body parts may have been wanted for “muti,” which refers to traditional medicine.
Traditional healers use both herbal remedies and magic, which may involve animal parts, in the belief that this will help their clients solve problems, obtain wealth or other benefits.
Ngoepe did not rule out the possibility of “muti” as a motive.
The three lions were worth 900,000 rand ($66,000USD), the newspaper Business Day reported.
The incident was the third of its kind since last year, when a total of three lions were beheaded in the same area, Ngoepe said.
“We cannot confirm that the same people are behind all these killings, but the modus operandi is the same,” he added.
No arrests have been made in any of the cases so far.