The incident happened at the rear of His Majesty’s Theatre on Skene Street, Aberdeen, at around 4.40pm on Wednesday.
Police said the boy was hit by a small dark Audi car which failed to stop following the collision.
The child sustained minor injuries and was taken to hospital for treatment.
Police are appealing for information about the incident.
Sergeant Peter Henderson of the Road Policing Department said: “We have already spoken to a large number of witnesses to this collision but I appeal to anyone who has information which would help us trace the vehicle and driver to contact Police on 101 quoting incident number PS-20190116-2501.
“Similarly I appeal directly to the driver of the vehicle involved to come forward.”