Alaba, out for three months earlier this season after a partial ligament tear in his right knee, was injured while playing for Austria in their 1-1 draw against Bosnia on Tuesday.
"I am bitterly disappointed," the 22-year-old told the club's website. "But I have a big aim and that is to be there at the season finale."
He is set to start rehabilitation work in about a month, Bayern said.
Alaba had been in superb form for Bayern since his comeback, helping them stay firmly on track for a treble of titles with some spectacular goals.
Bayern, who are top of the Bundesliga with eight games left and through to the German Cup last eight, face Porto in the Champions League quarter-finals later this month.
(Reporting by Karolos Grohmann; editing by Sudipto Ganguly)
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