"This person has been returned to Argentina. There is no place for violence in football", the police force wrote on Twitter.
Spanish news outlet AS, citing news agency EFE, named the fan as Maxi Mazzaro, a prominent figure in the Boca ultras group, which are known as Barras Bravas in South America.
The teams drew 2-2 in the first leg at Boca's ground but the second leg, originally scheduled to take place in Buenos Aires on November 24, was twice postponed after River supporters attacked Boca's team bus outside the Monumental Stadium.
Police said in a statement: "Police last night detected at Madrid's Adolfo Suarez Airport one of the most significant and unsafe Barras Bravas [ultra fans], who has a big criminal record".
South America's football federation, CONMEBOL, ruled River should lose the chance to play at home, with the game moved overseas amid fears of further fan violence.
Other Boca players appeared to have been affected by tear gas that police deployed to disperse the flashpoint and, after two delays to kick-off, the match was suspended.
The game was initially due to be played the following day, but was then postponed indefinitely as it became clear that Boca players needed more time to recover.
Both clubs have since protested the move to Madrid after numerous alternative venues were floated and veteran former Manchester City and Juventus star Tevez is keen for football to finally do the talking. River have a lot more pressure playing at home and now it is 50-50.
The bitter Buenos Aires rivals will meet at the Santiago Bernabeu on Sunday in the second leg of South American football's showpiece club clash.
Boca believe the chaos caused by River's fans means they should be awarded the trophy while River have protested against the loss of home advantage enjoyed by their opponents in the first leg, which finished 2-2.