Sirk is scheduled to undergo surgery Wednesday. The school has not set a timetable for his return.
The rising senior, who missed the 2013 season after tearing his right Achilles tendon, started 12 games last season and had 3,428 total yards -- the second-highest single-season total in school history.
With Sirk sidelined, Duke is expected to turn to backup Parker Boehme at quarterback. Boehme started one game last season in place of Sirk and saw action in nine games overall.
This is the third straight season that a key starter for Duke has sustained a major injury during offseason work. All-ACC linebacker Kelby Brown tore his ACL in both 2014 and 2015.