Riot police were seen entering a section of visiting fans towards the end of the second period, wearing protective armour and wielding security batons.
Some supporters wearing scarves over their faces were involved in scuffles with the police who lined the front two rows of the stand.
While there was no indication of what prompted the police reaction, Madrid had promised to step up police presence prior to the match after earlier clashes with Leicester City fans during last week's meeting between Atletico Madrid and the English champions.
"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.'"
Madrid won the game 4-2 after extra-time, progressing to the semi-finals with a 6-3 aggregate victory.