Mane was forced off after 20 minutes and the Senegal international will undergo an X-ray to determine the extent of the problem.
Senegal begin their World Cup campaign against the Netherlands on November 21 and also face hosts Qatar and Ecuador in Group A.
Bayern coach Julian Nagelsmann told a post-match press conference: "He took a blow to his tibial plateau. It's a painful spot.
"He'll have to have an X-ray to see what's happened."
Bayern's final game before the World Cup is at Schalke on Saturday.
Mane is Senegal's record scorer and scored the decisive penalty as his country beat Egypt to win the Africa Cup of Nations earlier this year.