Brown was injured late in a 21-10 win over the Green Bay Packers Sunday. Earlier in the contest, he had run 95 yards for a touchdown after recovering a fumble.
The Bears placed the five-year veteran on the injured reserve list Tuesday. Team officials said he will need six to seven months to fully recover from the injury.
"He's a special guy as far as a leader is concerned, but we have other guys that have to step up on the team," Bears Coach Lovie Smith said. "Sometimes you have guys waiting in the wings ready to take on that role when they're called upon."
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