The France international did the damage when shooting during a training session on Thursday and underwent surgery on Friday.
Bayern boss Hansi Flick said in a news conference that the former Lyon man will be sidelined for "at least three months".
It was reported by Bild that Tolisso could be out for up to six months, potentially ruling him out of the rescheduled European Championship - which starts on June 11.
The latest injury setback is a cruel blow for the 26-year-old, who was absent for nine months after he ruptured a cruciate ligament and the medial meniscus in his right knee in September 2018.
Bayern head coach Flick said on Friday: "I spoke to him on the phone this morning. He's already had an operation today.