The Peruvian scored in Sunday's home win over Hannover, but he will now miss games against champions Borussia Dortmund and lowly Augsburg for slapping Emanuel Pogatetz.
The incident was missed by the officials at the time, but the German federation handed out the ban after reviewing television footage.
Pizarro's opener in the 3-0 win was his 16th Bundesliga goal of the season, putting him joint-third in the league's scoring charts with Dortmund's Robert Lewandowski and behind Schalke's Klass-Jan Huntelaar and 21-goal leader Mario Gomez of Bayern Munich.
