The team says Posluszny will remain in Jacksonville for treatment and could be back at practice soon.
Second-year player Nate Stupar is expected to start in Posluszny's place against the Bears.
Posluszny has led the team in tackles the last three years, including a career-best 231 in 2012. He ranked second in the NFL with 161 tackles last season.
Posluszny's absence means the Jaguars will be without two starting linebackers in their second preseason game. Dekoda Watson, signed in free agency to replace Russell Allen, is on the physically unable to perform list while he recovers from groin surgery.