The German club said police action on Tuesday during half time at the Santiago Bernabeu was "completely misplaced and excessive" and have requested an explanation from Spanish authorities.
Eye-witnesses said that riot police stormed the visitors' section of the ground to remove a banner, which led to Bayern fans attacking officers, who replied in kind.
Riot police clash with Bayern fans in the tribunes at the Santiago Bernabeu stadium in Madrid on Tuesday. Photo: AFP
About 4,500 Bayern fans travelled to watch the Germans bow out 6-3 on aggregate, after going down on the night 4-2 in extra time in the quarter-final second leg.
Security was boosted in the Spanish capital ahead of the quarter-final second leg, which was declared "high risk" as is common for high profile Champions League games, after several European ties have been marred by violence.
There were clashes last week in the heart of Madrid between Leicester City supporters and police before the English side's Champions League quarter-final at Atletico Madrid.
Cristiano Ronaldo scored a controversial hat-trick to become the first man to reach 100 Champions League goals as Real Madrid overcame 10-man Bayern Munich 4-2 after extra time in Tuesday's thrilling quarter-final second leg.
The holders surged through 6-3 on aggregate at an exhilarated Santiago Bernabeu to take their place in Friday's semi-final draw for a record seventh consecutive year.