Coach Jason Garrett said Wednesday an MRI showed ligament damage that will require surgery in the next week or so, ending hopes of Lee returning in four to six weeks.
Lee also calls the defensive signals for the Cowboys. The Cowboys have signed veteran linebacker Ernie Sims, who played 13 games last year for Indianapolis.
Dan Connor, a free agent addition in the offseason, took most of Lee's playing time in the second half of last week's 19-14 win at Carolina. Connor is listed as a starter alongside Bruce Carter in the middle of the Dallas defense, with Sims backing up Connor.
Garrett said he expects Lee's leadership role to shift from the field to the sideline when the New York Giants visit Sunday.
"I can't tell you how well he's been playing since he's been our starting inside linebacker," Garrett said. "He's a bell cow for us and a guy that really everybody on our defense and football team looks up to." Lee missed a game and a half last year with a dislocated wrist and played several games in a cast.
The Cowboys moved up in the draft to take Lee in the second round out of Penn State in 2010. He started 15 games last year, finishing with 105 tackles and tying for the team lead with four interceptions. He had 58 tackles in six games this year and another interception.
"A lot of teams around this league have had significant injuries to significant players," Garrett said. "This is not new. This has happened a lot. And you rally around it." Dallas also put punter Chris Jones on injured reserve and signed safety Charlie Peprah. The Cowboys added linebacker Jerry Brown to the practice squad a week after he was let go by Indianapolis.