The 31-year-old suffered the injury on Tuesday and will be completely out of action for at least a month before he can start rehabilitation.
“The bone needs to be screwed together, which means four weeks until it heals, followed by rehab training,” confirmed Bayern coach Hansi Flick, who added the injury came as a shock.
According to German daily Bild, Perisic was hurt in a tackle from right-back Alvaro Odriozola, a new signing on-loan from Real Madrid.
The news is a blow for the league leaders, who host Hoffenheim in the third round of the German Cup later on Wednesday.
They then face Leipzig, who are second by only a point in the table, this weekend in a league showdown at the Allianz Arena.
Perisic can play as either a winger or striker, crucially as back-up to top-scoring forward Robert Lewandowski, and had started half of Bayern’s league games so far this season.
He scored a goal and set up another in his side’s 4-0 thumping of Hertha Berlin a fortnight ago and has a habit of contributing key goals or assists.
“He was in very good form and did us a great service in terms of his dynamism and experience,” added Flick.
There is some good news on the injury front with France defender Lucas Hernandez in the squad to face Hoffenheim after three months out with an ankle injury.
Flick said Kingsley Coman, who has been sidelined since suffering a knee injury in the 3-1 win over Tottenham in the Champions League last December, could be in the squad to play Leipzig.
The Bavarian giants play Chelsea in the last 16 of the Champions League and are chasing an eighth straight Bundesliga title.
