Trebek, 71, is the host of "Jeopardy," the TV quiz show in which contestants must give their answers in the form of questions.
The San Francisco Chronicle reported Trebek appeared on crutches when he served as host of the National Geographic World Championship geography bee at Google Inc.'s Mountain View headquarters Wednesday.
"What is, it happened at 2:30 a.m., chasing a burglar down the hallway of my San Francisco hotel when my Achilles tendon ruptured and I then fell on carpet, bruising the other leg in process. Surgery on Friday," Patch.com quoted Trebek as saying of the early-morning incident.
San Francisco police told the Chronicle a 56-year-old woman was arrested and charged with burglary and receiving stolen property. She allegedly stole wallets and purses from the room of the victim, whom police did not identify, the newspaper said.
The name of the hotel also was not disclosed.