He said he was injured while trying to chase down a woman who broke into his hotel room in San Francisco early Tuesday morning.
The 71-year-old is expected to be in a cast for six weeks.
The accused burglar, 56-year-old Lucinda Moyers, was arrested. She allegedly stole cash, a bracelet and other items from Trebek's room.
A judge has ordered her to stay at least 150 yards away from Trebek.
