The teenager was held on suspicion of a racially aggravated public order offence, Greater Manchester Police said.
An investigation was launched after a message was directed at a Manchester United player.
The boy has been bailed pending further inquiries.
United and England defender Rio Ferdinand was left with a cut to his left eyebrow after being hit by a 2p coin while celebrating his team's last-gasp winning goal at the Etihad Stadium.
City fan Matthew Stott, 21, had to be restrained by goalkeeper Joe Hart as he tried to confront Ferdinand, and was arrested.
Police made nine arrests in all as tempers among rival fans boiled over and officers have appealed for anyone with information about hooligans throwing coins to get in touch.
Nine men will appear in court in January.
Source: PA