The 25-year-old sustained the injury in his side's defeat to the New Orleans Saints at Soldier Field, weeks after the Bears lost Henry Melton to the same problem.
Head coach Marc Trestman told reporters: "Nate Collins is bad. He's got a torn ACL. It's a Henry Melton thing. He'll let it settle for a week. Then he'll have surgery. I'm very disappointed."
The Bears are 3-2 in their season after week five.