Police said 26-year-old David Campayo Lleo was arrested.
Spanish media are reporting he has been fired from a role on the coaching staff of one of Villarreal's youth teams after the arrest.
But Villarreal would not confirm nor deny reports about Mr Campayo Lleo's role with the club when questioned about their authenticity.
He faces from one to three years in prison if found guilty of charges related to racist provocation.
Villarreal has already banned Mr Campayo Lleo from the team's El Madrigal Stadium for life.
The Spanish league is expected to hand down punishment after the incident was listed in the referee's match report of Barcelona's 3-2 win at Villarreal on Sunday.
Alves picked up the banana and took a bite, provoking a social media campaign against racism in support of the Brazilian player, who is black.
Barcelona teammate Neymar was the first to post a picture of himself with a banana, leading to a flood of football players and other figures, celebrities and world politicians doing likewise.
Alves said if he had his way, he would post Mr Campayo Lleo's picture on the internet to shame him.
Villarreal said president Fernando Roig would be meeting supporters' groups to ensure such behaviour was not replicated after Alves called Spain "backward" and said there is "prejudice against foreigners because of race and colour".
The player has been subjected to racist taunts before, and black players Marcelo, Samuel Eto'o, and England's black players have also been on the receiving end of well-publicised racist behaviour by Spanish fans.