Bayern will have to shut "Sector 124" of the Allianz Arena for the quarter-final second leg on April 9, UEFA said, although they gave no indication of which part of the stadium that section is located in or how many seats will be affected.
UEFA said fans showed "an illicit banner" during the round of 16 tie at home to Arsenal earlier this month.
It declined to give more details about the cause of the ban, although media photographs showed a group of fans with a homophobic banner aimed at Arsenal, featuring Germany midfielder Mesut Ozil.
The German club have also been fined 10,000 euros, UEFA said.
Bayern said in a statement they would try to identify the culprits and sue them for damages.
"We regret this incident during the match against Arsenal and distance ourselves as far as possible from this discriminatory banner," said Bayern's CEO Karl-Heinz Rummenigge in a statement.
"This will never be accepted by Bayern Munich."
The banner appeared to be a direct reference to an Arsenal supporter group and featured an offensive cartoon of Ozil.
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- Bayern Munich