The Bundesliga champions have been punished after a homophobic banner was seen during the game against Arsenal
The banner referred to Arsenal as "Gay Gunners" and featured a crude drawing of the club's German midfielder Mesut Ozil.
The German champions have also received a €10,000 fine after their supporters committed the offence in the last-16 home leg against Arsenal on March 11.
"The Uefa Control and Disciplinary Body has decided to order the partial closure of the Allianz Arena," an official statement reads.
"In particular, the closure of sector 124 for Bayern's next Uefa competition home match, namely their Champions League quarter-final second-leg against Manchester United FC on 9 April.
"And to fine the German club €10,000 for the displaying of an illicit banner."
Bayern responded by promising action if the culprits are identified and insisted that the club wants nothing to do with the offending banners at the Allianz Arena.
"We regret this incident from the Arsenal match deeply and we dissociate heavily from this discriminating banner," club chief Karl-Heinz Rummenigge said in a statement.
"Bayern Munich will never accept this. Yet we have to accept Uefa's punishment. We will find the person who caused this and then we will check for the legal possibility on getting compensation from these people."