The 20-year-old Alaba has been ruled out for between six and eight weeks, although further tests will be carried out on Monday to investigate the full extent of the damage and decide what treatment will be given.
Full-back Rafinha also picked up an injury during the game and has torn ankle ligaments.
He will not need an operation, but will nevertheless miss the next four to five weeks, making him a doubt for the start of the season on August 25.
Both have been left out of the Bayern squad for their trip to China, according to the club's website.
Philipp Lahm and Bastian Schweinsteiger will also be left at home to concentrate on "building up their fitness" for the new season, according to coach Jupp Heynckes.