Carlo Ancelotti's side were beaten by Real Madrid after extra time
Baton-wielding officers clashed with away supporters at the Bernabeu, with Bayern labelling the police's behaviour as "misplaced and excessive".
A statement on the Bundesliga club's website read: "During half-time of FC Bayern's Champions League match at Real Madrid on Tuesday, there were violent attacks by Spanish police against FC Bayern Munich fans. FC Bayern find the Spanish police's actions misplaced and excessive.
"FC Bayern have already filed a complaint with UEFA against the actions of the Spanish police.
"In addition FC Bayern will request a statement about the actions from the Spanish police."
Bayern lost 4-2 after extra-time in the second leg of their quarter-final as Cristiano Ronaldo scored a hat-trick for Madrid, going out 6-3 on aggregate.
Spanish police also clashed with Leicester fans before the Foxes' quarter-final first leg against Atletico Madrid in the capital last week, although those incidents occurred ahead of the match.