Two officers sustained minor injuries, the statement released on Wednesday morning said. Police checked the identities of more than 300 people and issued dispersal orders.
According to the statement, the incident occurred on the evening before the match, which will be played on Wednesday at the Red Bull Arena, at around 8pm local time.
Approximately 300 high-risk fans of Rayo Vallecano were, according to police, moving together through the city centre, where clashes broke out with fans of Crystal Palace.
Rioting and objects thrown
The fans threw bottles, beer glasses and pub furniture, the statement continued. Officers immediately separated the groups of fans, and some police were also attacked in the process.
According to police, two officers were "slightly injured but remained fit for duty". Two people were also arrested, and the police operation ended at around 3:15am on Wednesday morning.
The fan festival, which at its peak saw around 2,000 visitors on the market square site, was "entirely peaceful throughout".