Collins sustained the injury after he was tackled on an interception return by Detroit offensive lineman Graham Glasgow during Sunday's 38-24 loss to the Lions.
The 28-year-old Collins has recorded 31 tackles, one sack and that one interception in six games this season since signing a four-year, $50 million contract in January.
"That's unfortunate," Browns coach Hue Jackson said.
"That's a big blow to our defensive football team. He's one of our best players and one of our leaders and one of our real good locker room guys. And we'll miss him. But that's football. It happens. He'll grow and get back as soon as he can and be stronger and better for it."
Collins was a first-time Pro Bowl selection in 2015 with the New England Patriots after amassing 89 tackles, a career-high 5 1/2 sacks and six passes defensed. He was a member of New England's Super Bowl XLIX-winning team in the 2014-15 campaign.
In five seasons, Collins has totaled 391 tackles, including 13 1/2 sacks, in 64 career games.