The 20,000 euro sanction on the Spanish has been imposed after fans sang racist chants and engaged in other racist behaviour during the Group C match against Italy in Gdansk on June 10.
Italy's black striker Mario Balotelli started in the 1-1 draw.
The Russians have been fined after being found guilty of the same charge in the Group A game against the Czech Republic in Wroclaw on June 8.
Czech right back Theodor Gebre Selassie, who is black, played in their 4-1 defeat.
Both associations can appeal.
Balotelli was also subjected to racist abuse by Croatia fans during a match on June 14 and the Croatian FA was fined 80,000 euros by European soccer's governing body.
The size of that fine was criticised by the Football Against Racism in Europe (FARE) network, who told Reuters there was public concern that Denmark's Nicklas Bendtner was fined 20,000 euros more for exposing an illegal advert on his underpants.
The Russian FA has already been fined three times for fan trouble at the tournament, including supporter violence.
UEFA said it would dock them six points in qualifying for the next European Championship if their fans were involved in further similar violence, with racist abuse not constituting a violent act under UEFA rules.
Holders Spain have reached Sunday's final being staged in Kiev while Russia went out in the group stage.