Leota will have surgery on Tuesday for the injury sustained early in last weekend's loss to LSU, Harsin said.
The Tigers are set to visit No. 2 Georgia on Saturday in their first road game of the season.
Harsin also confirmed previous reports that transfer quarterback Zach Calzada will undergo season-ending shoulder surgery. The former Texas A&M starter hasn't played this season.
A 6-foot-4, 257-pound graduate transfer, Leota has 17 tackles, including five tackles for loss and two sacks. He had seven sacks last season after transferring from Northwestern.
Auburn has switched to a 4-2-5 defense on the depth chart, with Derick Hall as the only starting edge rusher.
"Eku is a big loss," Harsin said. "He's an emotional leader. He's one of the smartest football players we have."
Harsin: Auburn's Leota, Calzada to undergo surgery originally appeared on NBCSports.com