Baldwin, 29, was described as "stupid" by Ospreys coach Steve Tandy after suffering the wound, which needed stitches, during a pre-match visit to a game park.
"There was an incident with a lion, but in fairness it was nothing to do with the lion. He did bite Scott but when you put your hand in a fence where there is a lion, then you will get bitten," Tandy told reporters after Friday's match.
"It was pretty stupid on Scott's behalf and he is pretty lucky... I don't know what sort of wildlife show Scott has been watching where you can pat a lion on the head as if it's a kitten.
"It's probably one of the silliest things I've even been involved in, but thankfully he is okay and hopefully he will be back up and running in the next couple of weeks."
The club confirmed in a statement that Baldwin had suffered the injury on Wednesday and said he had been treated at the scene by the team doctor before being admitted to a local hospital in Bloemfontein on Thursday for further treatment to prevent infection.
He will be released on Saturday morning to travel home with the rest of the squad as planned, Ospreys said. The Cheetahs beat the Ospreys 44-25 in Friday’s clash at the Free State Stadium.
(Reporting by Mark Gleeson; Editing by Toby Davis)
