The Peruvian is regularly utilised from the bench by coach Pep Guardiola, but his injury setback will see the German champions' attacking options limited.
Pizarro came on as a late substitute in Bayern's 2-1 victory over Borussia Dortmund on Saturday, yet the club confirmed on Wednesday that the 36-year-old is now set to be out for a lengthy spell.
"Pizarro has sustained a muscular tear in his right thigh and will be out for several weeks," they tweeted.
Pizarro's only goal of the current campaign came during Bayern's 4-1 DFB-Pokal win at Preussen Munster.
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