The club's vice-captain lasted just 17 minutes of the game before he was forced to limp off.
Tests carried out in Munich on Thursday have confirmed that part of the ligaments in his right ankle have been torn and his foot has been placed in a plaster cast.
He will have to wear the cast for a week before being given a special shoe to commence training in.
"We will have to make a prediction as to when Bastian will be able to train or play again at a later date," said Bayern's club doctor Hans-Wilhelm Muller-Wohlfahrt.
However, he will almost certainly miss Bayern's Champions League clash with Basel in just under a fortnight as well as Germany's friendly international against France a week later.
"I am really sorry about this latest setback for Bastian," said Germany's general manager Oliver Bierhoff on the website of the German Football Association (DFB).
"However, I am convinced he will be fit again come the end of the season and he will get back to his best for Bayern and the national team."