The 41-year-old man has been arrested on suspicion of a racially aggravated public order and remains in custody for questioning.
He is a Kier employee and has been suspended by the contractor.
Kier said: “Kier has a zero tolerance policy towards any racist and discriminatory behaviour.
“We can confirm an employee has been suspended pending an investigation.”
Police Superintendent Chris Hill of the City of Manchester Division said: “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.”