Gradkowski, who is entering his 10th NFL season, suffered the injury in the preseason opener against the Detroit Lions.
The Steelers could place Gradkowski on injured reserve for the second straight year or wait out the injury. Gradkowski missed all of 2015 with shoulder and hand/finger injuries. This offseason, he re-signed with the team on a one-year deal.
Landry Jones has solidified the No. 2 quarterback job behind Ben Roethlisberger, but behind him is project Dustin Vaughan, who has never taken an NFL snap and was cut in Dallas Cowboys camp last year.