"The fracture was successfully repaired and a plate inserted in an operation performed at around 02:00 on Thursday morning," said Bayern, after the player was injured during Wednesday's 3-2 win over Napoli in the Champions League.
Bayern said Schweinsteiger will stay in hospital until Friday and must rest completely for two weeks after that.
"The first step in his sports rehabilitation programme will be to resume jogging, before the player is cleared to resume training with the team in approximately six weeks.
"That in turn means Schweinsteiger will not play again this calendar year," it added.
"It's a blow, because he's been in outstanding form recently," said coach Jupp Heynckes.
"In the second half, we saw how important Bastian is to the team. Our game suffered badly after he went off."
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