Greater Manchester Police have arrested a 41-year-old man after a video posted on social media showed a supporter apparently making racist gestures during Saturday's Manchester derby.
"Police were called to a report of a supporter making alleged racist gestures and sounds towards players during the Manchester City and Manchester United derby," said Greater Manchester Police in a statement.
"A 41-year-old man has been arrested on suspicion of a racially aggravated public order and remains in custody for questioning."
City pledged to take a zero tolerance approach against supporters found to have subjected United players to racist abuse after the Premier League champions lost 2-1 to their local rivals on Saturday.
United midfielder Fred was hit by objects thrown from the crowd as he prepared to take a corner in the second half and footage on social media appears to show a City fan mimicking a monkey at the Brazilian.
United manager Ole Gunnar Solskjaer said both Fred and Jesse Lingard had been "affected" by the alleged abuse.
Superintendent Chris Hill of the City of Manchester Division said the force was taking the matter "extremely seriously".
"I would like to thank the public for their ongoing support with this incident," he said.
"Racism of any kind has no place in football or our society and I hope this arrest shows that we are taking this matter extremely seriously.
"We will continue to work with Manchester City and Manchester United Football Clubs on this incident and will investigate any other lines of enquiries."
The English Football Association will also investigate and is planning to talk to the clubs, referee Anthony Taylor, the police and other relevant parties.