Wide receiver Golden Tate also was injured in the game, suffering a concussion because of the way he landed on his 23-yard touchdown reception in the fourth quarter of the 19-14 loss at Chicago.
The 24-year-old Peppers, acquired in the offseason in the trade that sent Odell Beckham Jr. to the Cleveland Browns, suffered his injury at the end of the first half on a kickoff return. He leads the Giants with 78 tackles this season and also has an interception, which he returned for a touchdown.
Tate, 31, has 36 receptions for 450 yards and four touchdowns in his first season with the Giants after signing with the team in free agency.
Sunday’s loss was the Giants’ seventh straight, dropping their record to 2-9.