The incident took place as the player was about to take a corner in a match at Villarreal on Sunday.
Alves responded by taking a bite out of the banana – a gesture which was widely praised and sparked a large social media campaign against racism.
The man detained has been identified as a 26-year-old Villarreal supporter. According to local media, his name is David Campaya Lleo.
The club said earlier the man involved had had his season ticket withdrawn and been given a lifetime ban.
Alves told BBC Brasil on Wednesday it was “not an isolated incident”, and that he had been denouncing racist insults for six years.
“I hope that this (campaign) can be an alert to ban this kind of attitude from football altogether. I hope the debate about racial prejudice will not fade away, but stays on permanently and not be restricted only to football,” he added.