The team said Thursday the recovery period is four to five months.
Conte started all 16 games for the first time in his career last season, but struggled along with just about everyone else on defense.
His worst moment was when he failed to lock onto Green Bay's Randall Cobb in the closing minute of the final game. That led to a wide-open 47-yard touchdown pass from Aaron Rodgers on fourth down that gave the Packers a 33-28 victory and kept Chicago out of the playoffs.
AP NFL websites: www.pro32.ap.org and www.twitter.com/AP-NFL