Alves made international headlines for his response to the historically racist gesture -- he calmly picked up the banana and ate it before taking a corner.
"I don't know who it was, but thanks to whoever threw the banana, the potassium gave me the energy for the two crosses which led to a goal," he told reporters after Barcelona's 3-2 win.
The fan has since been identified as 26-year-old Villarreal fan David Campaya Lleo. The club has banned him for life and said in a statement that it "deeply regrets and condemns the incident."
Alves told Brazil's Radio Globo that the fan was part of Spain's "very backward" attitude toward foreigners.
"If I could, I would put a photo of the fan on the internet so that he would be shamed," he said Tuesday. "There is racism against foreigners. They sell the country as being first world but in certain things they are very backward."