The away side ran out 2-1 winners at the Allianz Arena and at full-time several spectators entered the pitch, one running towards Franck Ribery and almost bringing him down while being tackled to the ground by a steward.
Further invasions saw one supporter approach Toni Kroos, while others attempted to get selfies with the German and Cristiano Ronaldo.
Bayern are also in trouble for the displaying of an "offensive" banner in the stands and will find out their punishment on May 31.