"Following the charge of racist behaviour by Real Madrid supporters during the match (Article 14 of the UEFA Disciplinary Regulations), the Control and Disciplinary Body has ordered the partial closure of the Santiago Bernabeu for one match," European soccer's governing body UEFA said in a statement.
"More specifically, sectors 120 and 122 of the stadium will be closed for the club's next UEFA competition home game. Real Madrid are obliged to display a banner with the wording 'No to Racism' in those sectors."
Real beat Bayern 1-0 in the first leg on their way to a 10th European Cup crown.
Spanish football has been plagued by racist incidents this season, the most high profile involving Barcelona's Dani Alves, who took a bite from a banana thrown at him by a Villarreal fan during a La Liga match in April.
Villarreal were fined 12,000 euros by the Spanish soccer federation and the Anti-Violence and Racism in Sport Commission appealed the perceived leniency of the punishment.
Levante's Senegal midfielder Papakouli Diop complained of racist abuse from Atletico Madrid supporters this month and fans of Real Betis allegedly directed abuse towards one of their own players in November.