The injury occurred during a training session on Thursday with his club Bayern Munich.
"It's a serious muscle injury," said Bayern boss Hansi Flick. "On one shot he felt intense pain, there were no warning signs."
Tolisso, 26 joined Bayern from Lyon in 2017 for 41.5 million euros.
Since then he has won 10 titles with the team including the haul of six trophies between June 2020 and February 2021.
""In recent games, he has again shown his quality and I'm more than impressed by him.
"He'll be given all the time he needs and he has our full support in the coming weeks and months to bring him back to his best level," Flick added
Games
The 26-year-old had already missed six games this season due to two different muscle injuries.
Though he has made only seven starts in 22 Bundesliga matches this campaign, he was likely to feature in the coming months as Bayern hunt a record-extending ninth successive Bundesliga title as well as defend the DFB-Pokal and their Champions League crown.
Even if he were to recover ahead of schedule, he is unlikely to gain a place in the France squad for the European championships.
They were scheduled for last summer but due to the coronavirus pandemic were reprogrammed to take place between 11 June and 11 July.
