Zaha, 27, shared the obscene messages on Twitter before the match and Villa said they would investigate the incident with police.
After Villa’s 2-0 win over Palace, a police statement read: “We were alerted to a series of racist messages sent to a footballer today and after looking into them and conducting checks, we have arrested a boy.
“The 12-year-old from Solihull has been taken to custody. Thanks to everyone who raised it. Racism won’t be tolerated.”
Earlier, Villa responded with a social media post: “We deplore the disgusting racist messages sent to Wilfried Zaha.
“We condemn all forms of racial discrimination and stand with Crystal Palace. We are working with the police in investigating this extremely serious matter and when the culprit is identified AVFC will issue a lifetime ban.”
Palace also supported Zaha with a statement: “This is an absolute disgrace and should not be happening. We stand with you, Wilf, and anyone else who has to suffer such horrific abuse.”
Before the match, Palace manager Roy Hodgson was asked about the incident and told Sky Sports: “It is very saddening on the day of a game that a player wakes up to this cowardly and despicable abuse.
“I think it is right that Wilf made people aware of it; I don’t think it is something he should keep quiet about.
“I think it is very good that our club, Aston Villa and the Premier League are doing everything they can to find out who this despicable individual is and one can only hope that they will get identified and they will get called to account and they will pay for these actions.
“There is literally no excuse; there is no excuse at all.”
Before kickoff, both sets of players took the knee to support the Black Lives Matter movement.
Since the Premier League returned from the suspension caused by the coronavirus pandemic, playing and coaching staff have taken the knee to show their support for the campaign.
A Premier League statement read: “This behaviour is completely unacceptable and the Premier League stands alongside Wilfried Zaha in opposing this, and discrimination in any form. There is #NoRoomForRacism, anywhere.
“We will continue to support players, managers, coaches and their family members who receive serious discriminatory online abuse.
“Through our dedicated reporting system we can take immediate action on cases like this.”