Zaha revealed he had received several abusive messages on social media before Sunday’s trip to Aston Villa.
“cowardly and despicable” his manager Roy Hodgson said.
The Premier League also said it is “completely unacceptable”.
West Midlands Police tweeted Zaha to say they would look into the abuse and hours later confirmed an arrest.
“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,” read a WM Police tweet.
“The 12-year-old from Solihull has been taken to custody. Thanks to everyone who raised it. Racism won’t be tolerated.”