Mueller, who was returning to top form under new coach Jupp Heynckes after being left on the bench often by Carlo Ancelotti, had set up Corentin Tolisso's 52nd-minute winner before being taken off injured soon afterwards.
"The Germany international will be out for an expected three weeks," Bayern said in a statement.
This means he will miss the German Cup clash with RB Leipzig this week as well as the weekend league game against the same opponents.
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Mueller will also sit out the Champions League group game at Celtic on Oct. 31 and the league match against Bundesliga leaders Borussia Dortmund.
Bayern are second in the standings, level on 20 points with Dortmund but with an inferior goal difference.
(Reporting by Karolos Grohmann, editing by Ed Osmond)
