The Bavarians will have to make do without the veteran forward for over a month after he suffered a thigh muscle injury
The veteran striker, who has been used sparingly this season, joins the likes of Xherdan Shaqiri and Holger Badstuber on the slidelines and is set to miss the showdown with Borussia Dortmund next month.
That leaves Pep Guardiola with only one orthodox striker at his disposal, Mario Mandzukic, though the Spaniard has deployed Thomas Muller up front.
However, summer signing Thiago Alcantara, who has been missing since the opening weeks of the season, has returned to training following an ankle injury.
Bayern Munich, who overcame Viktoria Plzen 5-0 in the Champions League on Wednesday, entertain Hertha Berlin this weekend.
Pizarro, 35, who is currently enjoying his second spell with the Bavarian club, has scored three goals in his six appearances this term.