Varty, 61, was filming at his private game reserve near Philippolis in South Africa's Free State when he was attacked by the animal and is now receiving treatment at a local hospital.
He sustained multiple puncture wounds and two broken ribs and underwent a six-hour emergency operation, but is still in a serious condition.
Amanda Appelgryn, spokeswoman for the Mediclinic hospital in Bloemfontein, says, "He went for six-hour surgery and is in the intensive care unit. He had lost a lot of blood and got a transfusion in theatre. He has multiple injuries on his front and back and all over his whole body, but not his face.
He is conscious... he is in pain but he's doing OK... He's not stable and he's not critical, but somewhere inbetween. It's best to say he's in a serious condition. I can't say he's out of danger: with wild animals there is always the possibility of infection."
Varty has produced more than 30 wildlife documentaries during his career and he found success in Hollywood by writing and starring in 1990 film Running Wild with Martin Sheen and Brooke Shields.