Riot police clashed with Bayern fans inside the Santiago Bernabeu, having entered the section of the ground housing the away supporters towards the end of the first half.
A number of fans, many of them wearing scarves over their faces, were caught up in scuffles with the officers as they began lining the front two rows of the tier. There was no immediate indication of what prompted the police response.
A statement released by Bayern on Wednesday read: "During the half-time break of Bayern Munich's Champions League match at Real Madrid on Tuesday(Wednesday morning AEST) , Bayern Munich's fans came in for some violent attacks by the Spanish police.
"FC Bayern felt the action of the Spanish police [to be] completely misplaced and immeasurable. FC Bayern have already filed a complaint with UEFA against the actions of the Spanish police.
"In addition, FC Bayern will request a statement from the Spanish police about the events."
Following the clashes between Leicester City supporters and officers that preceded last week's quarter-final first leg between Atletico Madrid and the Premier League champions, authorities in the Spanish capital pledged to reinforce its police presence for Bayern's visit.
"Nearly 1,800 officers will ensure that the match is held normally and that security is reinforced in and outside the stadium," Madrid's city hall said in a statement this week. "The police presence will also be reinforced in tourist areas of the capital."
A Cristiano Ronaldo hat-trick gave Madrid a 4-2 extra-time win over Bayern, sealing a 6-3 aggregate triumph for the European champions.