The penalty comes after widespread support from celebrities and public figures for the Brazil defender, who picked up the banana and took a bite as he prepared to take a corner during the match on April 27.
Alves later told Brazil's Radio Globo that Spain was "very backward" in its approach to racism.
Villarreal responded quickly by banning the supporter for life but the club have now been fined by the federation as Spanish football tries to clean up the game's image.
That aim was not helped by allegations last weekend from Levante's Senegal midfielder Papakouly Diop who complained of racist abuse by visiting Atletico Madrid supporters.
"We have accepted the 12,000 euro fine," a Villarreal spokesman told Reuters. "The federation were though pleased with the quick and positive action that the club took by identifying the fan."
($1 = 0.7177 Euros)