Sterling, 23, was reportedly kicked and racially abused as he arrived at City’s Etihad complex ahead of last Saturday’s match against Tottenham Hotspur.
Police said on Tuesday a 29-year-old man was arrested on suspicion of racially aggravated assault.
He is in police custody for questioning over the alleged hate crime.
Detective Chief Inspector Paul Walker from Greater Manchester Police (GMP) said: “Earlier this morning we arrested a 29-year-old man after investigating a racially aggravated assault in Manchester.
“Racism will not be tolerated in Greater Manchester and has no place in civilised society.
“We take every report incredibly seriously and any reports can be reported via the True Vision website www.report-it.org.uk “
Kick It Out, football’s equality body, said it had been in touch with Sterling to offer him support.
Anyone with any information about the incident should contact police on 101 or the independent charity Crimestoppers, anonymously, on 0800 555 111.