He was replaced by veteran Jordan Devey.
Duvernay-Tardif was on crutches in the locker room after the game with a bulky brace on his left leg.
The Chiefs already are playing without one starting offensive lineman, center Mitch Morse, who has a sprained foot.
"It's hard to see one of our guys go down," Chiefs backup center Zach Fulton said, "but we're all interchangeable as a unit. 'Next man up,' that's our mantra."
If Duvernay-Tardif is lost for a long period, one possible replacement is Parker Ehinger. He was a starting guard for the Chiefs last year, before his season ended prematurely because of a knee injury.
Duvernay-Tardif joined the Chiefs as a sixth-round draft pick in 2014 out of McGill University in Montreal. Duvernay-Tardif, a medical student at McGill, signed a five-year contract extension with the Chiefs last winter worth about $41 million.
Information from The Associated Press was used in this report.