Riot police equipped with protective masks, armour and security batons were seen entering a section of visiting supporters towards the end of the first half of Tuesday's quarter-final second leg.
A number of fans, many of them wearing scarfs over their faces, were caught up in scuffles with the officers as they began lining the front two rows of the section of the stand.
There was no immediate indication of what prompted the police response.
"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 4-2 after extra-time to progress to the semi-finals with a 6-3 aggregate victory.