Michigan officials declined to discuss specifics regarding Kovacs' injury, but said he also is questionable for the Nov. 5 game at Iowa.
Michigan is No. 18 in the BCS standings, and ranked No. 17 in the AP Top 25.
Kovacs leads the Wolverines (6-1, 2-1 Big Ten) with three sacks and is third on the team with 42 tackles. He is tied for 19th on the school's all-time tackles list with 233.
The 6-foot, 197-pound redshirt junior was named one of 20 quarterfinalists for the Lott IMPACT Trophy Wednesday, given to college football's defensive player of the year for his play and character.
Senior cornerback Troy Woolfolk will start in place of Kovacs at safety. True freshman Blake Countess will start at corner.
Purdue is 4-3, 2-1 in the conference.
Michael Rothstein covers University of Michigan sports for WolverineNation. He can be reached at firstname.lastname@example.org or on Twitter @mikerothstein.