Gerardo Martino's men came from behind to claim all three points at El Madrigal in La Liga, but the game was marred by an incident in the 76th minute as a fan threw a banana at the feet of Alves as he prepared to take a corner.
However, the Brazil international offered a light-hearted retort, picking up and eating the banana as he took the set-piece instead of throwing it away.
The 30-year-old insisted afterwards that humour is the best way to deal with racism, jokingly thanking the fan in question for giving him "the energy for the two crosses which led to a goal".
And the Catalan club have now given their backing to the former Sevilla man, while also commending Villarreal for immediately condemning the actions of the supporter.
A statement on the club's official website read: "FC Barcelona would like to underline the civil, cultural, social and sporting importance of two messages which UEFA remind us of before every game: Respect and No to Racism.
"FC Barcelona wishes to express its complete support and solidarity with our first-team player Dani Alves, following the insults he was subject to from a section of the crowd at El Madrigal on Sunday during the game against Villarreal.
"FC Barcelona accepts that the perpetrators of these insults are in no way connected to Villarreal and we value very positively the support the club offered to our player.
"The club's immediate condemnation of the incidents is a step in the right direction to firstly isolate and then eradicate completely from the sporting arena this kind of behaviour.
"FC Barcelona reiterates its support for UEFA's message of Respect and No to Racism and urges all clubs to continue fighting against the blight on the game which any kind of aggression against a sportsperson on the basis of their race represents."
