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.
The striker is yet to find the net in the Bundesliga this season, having made five appearances.
Pizarro's only goal of the current campaign came during Bayern's 4-1 DFB-Pokal win at Preussen Munster.
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