Coach Hugh Freeze confirmed Nkemdiche's injury to ESPN.com and said that Nkemdiche underwent ankle surgery Sunday.
Nkemdiche, who had recorded 28 tackles and a sack in seven games this season, injured his ankle in the first quarter of Saturday's game and did not return. He was seen wearing a walking boot in the second half of the game.
The former freshman All-American and two-time All-SEC second-team member has 145 total tackles and four sacks during his career.
Senior Serderius Bryant will replace Nkemdiche at his outside linebacker spot. Bryant, who has four starts this season, led the Rebels with 78 tackles, 12 tackles for loss and three forced fumbles in 2013.
His brother, defensive tackle Robert Nkemdiche, and former All-American safety Cody Prewitt also missed time late against LSU with unspecified injuries. Left tackle Laremy Tunsil left the game with a pulled right biceps but later returned. Freeze said they are "day-to-day."
No. 7 Ole Miss (7-1, 4-1 SEC) hosts No. 4 Auburn (6-1, 3-1) on Saturday at 7 p.m. ET. The game is scheduled to air on ESPN.