Sutton suffered the injury as he leaped to make a catch in positional drills about 30 minutes into the workout and landed awkwardly. He briefly stayed on the ground before eventually walking off the field with trainers and going inside the Broncos' complex.
The third-year receiver, who played in his first Pro Bowl last season as an injury replacement for DeAndre Hopkins, was then taken for an MRI, sources told ESPN.
His is questionable for the Broncos' opener on Monday Night Football against the Tennessee Titans.
Denver lost linebacker Von Miller for an extended period of time -- possibly the season -- with an ankle injury in Tuesday's practice. Linebacker Bradley Chubb, who is returning from a torn ACL, has been limited in practices with knee soreness.
Sutton, who led the Broncos last season with 72 catches and 1,112 yards, is a vocal leader on one of the league's youngest offenses as he enters his third season. He is the only receiver on the current roster who has had more than 30 catches in any season with the team.
Less than an hour before Thursday's practice Sutton expressed confidence that despite the installation of a new playbook and the team's inexperience on offense, the Broncos could be productive early in the season.
"It's going to be a lot of fun,'' Sutton said earlier Thursday. "We understand that there are things that we can't control and couldn't control that put us in this spot, but I don't have anything that's on me that makes me have any concern or any worry.
"I'm more excited than anything because I've seen it. I've seen how it looks whenever we're clicking the way we're supposed to. I've seen how it looks and how explosive it can be. I'm just really excited to see it come to fruition on Monday."