Manchester City said they were investigating a fan for alleged "racial gestures" made during Saturday's 2-1 derby defeat to Manchester United at the Etihad Stadium.
Television images circulating on social media showed a City fan making a gesture in front of United's Brazilian midfielder Fred during the Premier League game.
"Manchester City FC are aware of a video circulating on social media which appears to show a supporter making racial gestures during the second half of the match against Manchester United this evening," the club said.
"Officials from the club are working with Greater Manchester Police in order to help them identify any individuals concerned and assist with their enquiries."
The club said they were also working with police to identify fans who threw objects on to the field when Fred was taking a corner in front of them.
Fred appeared to have been struck by at least one object.
"The club operates a zero tolerance policy regarding discrimination of any kind, and anyone found guilty of racial abuse will be banned from the club for life," added the City statement.
United manager Ole Gunnar Solskjaer said midfielder Jesse Lingard had also been targeted.
"I've seen it on the video, it was Jesse and Fred and the fella must be ashamed of himself. It's unacceptable and I hope he will not be watching any football anymore."
Anti-racist campaign group Kick it Out said on Twitter that they had received a high number of complaints about incidents at the game.
"We have been inundated with reports of alleged racist abuse from a number of individuals during this evening's Manchester Derby," said the group.
"We will be contacting both clubs to offer our support and hope swift action is taken to identify the offenders."