United’s 3-1 win over the champions at the Etihad Stadium left Pep Guardiola’s men 14 points behind leaders Liverpool while Ole Gunnar Solskjaer’s men moved up to fifth, five points behind fourth-placed Chelsea.
The game was temporarily halted in the 68th minute as Fred went to take a corner and was struck by an object thrown from the crowd.
A man could be seen making monkey gestures just behind the advertising board close to the corner flag with a video of the incident going viral after the game.
A statement from the Police force read: "At around 6.55pm on Saturday 7 December 2019 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.
"A 41-year-old man has been arrested on suspicion of a racially aggravated public order offence and remains in custody for questioning."
Superintendent Chris Hill of the City of Manchester Division added: "I would like to thank the public for their ongoing support with this incident.
"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."
Manchester City have already made clear their intentions of banning for life anyone found culpable in the incident.
