Greater Manchester Police have confirmed the youngster has been apprehended and bailed on suspicion of a racially-aggravated public order offence following Sunday's match
The investigation was launched when police were notified of a racist tweet which was sent to a Manchester United player, reported to be defender Rio Ferdinand, following Sunday's game, which the Red Devils dramatically won 3-2.
A statement from Greater Manchester Police read: "Police investigating a racist tweet sent during Sunday's Manchester derby have made an arrest.
"An investigation was launched following a message directed at a Manchester United player.
"A 15-year-old boy was arrested on suspicion of a racially aggravated public order offence on the evening of Monday 10 December 2012.
"He has been bailed pending further enquiries."
The boy has been bailed pending further enquiries as the fallout from a particularly heated clash at the Etihad Stadium continues to intensify.
Nine arrests were made in the immediate aftermath of the fixture, and authorities are still searching for the man who threw a coin which struck Ferdinand in the face as he celebrated his side's victory.
Meanwhile, Manchester City fan Matthew Stott is facing a life ban from the club after running onto the pitch in an attempt to get to the United star.