The fan in question was issued with a lifetime ban from Villarreal following the incident against Barca on Sunday.
During the Catalan giants' 3-2 victory at the Estadio El Madrigal, a banana was thrown onto the pitch as Alves lined up to take a corner kick.
In response to the alleged racist attack, Alves unpeeled the banana and took a bite out of it before delivering his kick from the corner flag.
A police spokesperson has now confirmed to the Spanish media that a person has been detained following the incident at the weekend.
A number of footballers around the globe have given their support to Alves on social media by posing for photos holding bananas and using the hashtag #weareallmonkeys.