The use of technology in German football has been met with opposition from the stands and Bayern fans vented their frustration in Wednesday's quarter-final clash at Allianz Arena.
The banner read: "Modern football kills emotion. F*** VAR! F*** UEFA!"
Bayern have also been charged with 'kit infringement' after Leon Goretzka wore the wrong shirt in the 3-1 second-leg loss.
Article 28 of the UEFA Equipment Regulations states that teams are prohibited from advertising more than one sponsor on shirts worn in European competitions.
The cases will be heard by the UEFA Control, Ethics and Disciplinary Body on May 16.
Zenit were also hit with damages charges for actions during their last-16 tie with Villarreal.
The draw for both the Champions League and the Europa League quarter-finals took place on Friday, with Liverpool drawn against Porto and Juventus drawn against Ajax. Premier League rivals Tottenham and Manchester City will also face off, while Barcelona and Manchester United were pitted against one another in a clash of European giants.