Fisher is scheduled for surgery on Thursday in Philadelphia to have the injury repaired.
Cam Erving will replace Fisher in Sunday's game against the Ravens at Arrowhead Stadium.
The Chiefs said Fisher had a groin injury after he injured himself in practice on Friday. He was listed as questionable on the injury report for last week's game against the Raiders.
Fisher started but played just four snaps before being pulled in favor of Erving.
"I thought Cam did a good job," coach Andy Reid said. "He had a solid game. He started off a little shaky at the beginning, but after that he finished up real well."