David Lees, of Heathbank Road, Blackley, died in hospital after being found collapsed on Middleton Road in Prestwich at 0100 BST on Saturday.
The 23-year-old's death followed a disturbance believed to have involved white and Asian men.
A 25-year-old has been arrested on suspicion of Mr Lee's murder.
"It seems like a disturbance has escalated out of all proportion"
About 20 people were seen arguing on the forecourt of a BP garage prior to the killing.
Mr Lees, who was white, had been among people involved in a row with a group of Asian youths.
The police spokesman said: "We are treating this as a racial incident, but the murder was not racially motivated."
Supt Mark Robinson of Greater Manchester Police added: "He (Mr Lees) was run down and killed by a vehicle.
"That vehicle fled the scene and we are treating it as a murder inquiry.
"It seems like a disturbance or a low-level disorder has escalated out of all proportion."
Friends and family of the victim have left flowers and tributes at the scene, which was sealed off until mid-morning while investigations were being carried out.
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