Three experienced handlers were working with the grizzly Tuesday at the Predators in Action wild animal training center when the bear attacked Stephan Miller, 39, said San Bernardino County sheriff's spokeswoman Cindy Beavers.
Stephan Miller is the cousin of training center owner Randy Miller, she said.
Pepper spray was used to subdue and contain the bear, and there were no other injuries, Beavers said.
The state Department of Fish and Game and Occupational Safety and Health Administration were investigating.
Sheriff's Sgt. Dave Phelps said the bear was a 5-year-old male named Rocky. The Predators in Action Web site said Rocky is 7½ feet tall and weighs 700 pounds.
The Web site identified Rocky as the animal that appeared with Ferrell's character in the scene from "Semi-Pro." Randy Miller doubled for Ferrell in the bear wrestling match, according to the site.
The attack took place during videotaping of a promotional video, said Harry Morse, a spokesman for the California Department of Fish and Game. There was no immediate indication Wednesday who had custody of the tape.
Morse said the animal center had a good safety record. It had received a single misdemeanor citation in 1999 after animal rights groups complained that owner Randy Miller had arranged to have another bear wrestle a man. He received a permit from Los Angeles County officials for the exhibition but it still was a violation of state law, Morse said.
There was no word whether the bear would be euthanized because of the attack. Morse said the attack occurred outside the agency's jurisdiction. Representatives of the county's Animal Care and Control Program did not immediately respond to a call seeking comment Wednesday.
Calls seeking comment from Randy Miller were not immediately returned Tuesday evening.
The center, located in the San Bernardino Mountains east of Los Angeles, has two grizzlies, and also trains lions, tigers, leopards, cougars and wolves for uses ranging from film and TV to advertising and education.
In a February interview, Randy Miller called Rocky "the best working bear in the business," The Sun of San Bernardino reported Wednesday. But the paper quoted him as adding: "If one of these animals gets a hold of your throat, you're finished."
Randy Miller won a World Stunt Academy Award for his work wrestling tigers in the 2000 blockbuster "Gladiator" and performed stunts with his animals in films including "The Postman," "The Island of Dr. Moreau," and "The Last Samurai." He also helped recreate animal attacks for National Geographic documentaries and the Discovery Channel.
It was not immediately known how long Rocky has been at the facility.
The attack prompted actress Virginia McKenna, founder of the international wildlife charity Born Free, to call for the entertainment industry to stop using wild animals.
"The movie industry urgently needs to use its technological and creative imagination to put an end to the use of live wild animals in commercials and movies," McKenna, who starred in the 1966 wildlife film "Born Free," said in a statement. "Hollywood is a dream factory - this time the dream has become a nightmare."
Native grizzly bears are extinct in California.