Dortmund confirmed the injury in a statement on Sunday, saying Can "will be out for an extended period."
Can clutched his left knee after tussling with Bayern's Konrad Laimer just before half-time. The former Liverpool and Juventus midfielder played on for a few minutes but then signalled to the bench and was withdrawn.
Dortmund feared a serious knee injury after the match and sporting director Sebastian Kehl said Sunday the club's worst fears were confirmed.
"Emre's injury is extremely bitter. Not just for him, but for all of us.
"He is our captain, always puts the team first and is an important part of our club. Emre will receive all our support in the coming months so that he can make a full recovery."
Can joined Dortmund from Juventus in 2020 and was promoted to captain ahead of the 2023-24 season but his current contract at the club expires in the summer.
The injury ends the 32-year-old's hopes of making the Germany squad for the World Cup in the summer. Can has 48 Germany caps, scoring two goals, but had not played at an international level since September 2024.