The incident occurred at around 5am on Saturday on the Route du Pont Butin in the suburb of Lancy as the cyclist was heading south on the arterial road, the Tribune de Genève newspaper said on Tuesday.
He was struck from behind by the vehicle driven by the suspect in the same direction, cantonal police said earlier.
The victim was catapulted a distance of seven metres from the impact, the Tribune said, citing a justice department spokesman.
The driver of the car, accompanied by three passengers, left the accident scene and was arrested later, the daily said.
He had been returning from a nightclub in the city of Geneva.
The driver faces several charges in addition to the murder allegation, including driving under the influence of alcohol and failure to remain at the scene of an accident to assist a victim.
His detention has been authorized for two months while an investigation continues.
Geneva police earlier issued a call for witnesses who may be able to shed light on the collision.
The death marked the seventh fatality on Geneva roads so far this year, police said.