The 24-year-old scored twice in Bayern's 4-0 victory at Hannover on Sunday but was withdrawn after an hour, with medical tests subsequently revealing a hamstring pull in his right thigh.
In a statement published on fcbayern.de, club doctor Hans-Wilhelm Muller-Wohlfahrt announced Muller would take a "mandatory five-day break" and ruled him out of Saturday's Bundesliga game with Schalke.
The Germany international will therefore hope he can recover full fitness in time for the last-16 second-leg encounter with Arsenal in Munich on Tuesday, March 11.
Bayern won the first leg 2-0 at the Emirates Stadium through goals from Muller and Toni Kroos.
The record German champions also announced that winger Franck Ribery has stepped his recovery following buttock surgery while midfielder Xherdan Shaqiri is back in training after a thigh injury.