He was placed on injured reserve on Tuesday.
"That's a big blow to our defensive football team," coach Hue Jackson said.
Jackson did not specify the degree of Collins' injury and only said there was "damage." Collins will not need surgery, Jackson said.
Collins was injured when he was tackled on an interception return in the first quarter. Offensive lineman Graham Glasgow grabbed Collins around the shoulders and twisted him to the ground. As he did, Collins' knee was caught under Glasgow's body.
The fifth-year linebacker finishes the season with six starts, 31 tackles, one sack and one interception. He missed three games earlier this season with a concussion.
In the offseason, the Browns kept Collins off the free-agent market by signing him to a four-year, $50 million contract. The Browns acquired Collins from the New England Patriots last season via trade.
James Burgess, an undrafted free agent out of Louisville, will take Collins' place.
The Associated Press contributed to this report.