Badstuber suffered the injury during Bayern's 6-1 rout of Porto, which saw them qualify for the Champions League semi-finals.
The 26-year-old is set to be out of action for four months, but vowed to come back fitter and stronger than ever.
"Despite it all I'm remaining positive and I'll be back again fully fit," he was quoted as saying on Bayern's official site. "I know everything will be done for me at FC Bayern so I can come back as an important part of the team."
Badstuber only recently regained his spot in the Bayern squad and German national team since he was out for 17 months following an anterior cruciate ligament injury in December 2013.
As a result of his injuries, Badstuber has only played 16 games this season.
"We're so sorry for Holger," Bayern CEO Karl-Heinz Rummenigge said. "He worked so hard towards his latest comeback – and now this.
"We've come to know and value Holger as a fighter. He'll never allow himself to become discouraged even by this new injury. He knows how important he is to us. That will spur him on during the sports rehabilitation phase and help him recover fitness as quickly as possible."