The boy, who has not been named, was hit by the car in Ashton-under-Lyne earlier on Monday.
Greater Manchester Police said the driver of the car failed to stop at the scene in Moss Street West at its junction with Mowbray Street.
The car is believed to be a black or grey-coloured Mercedes A or B class, and may have damage to its front near-side headlight, the force said.
Sgt Paul Higgins, of the serious collision investigation unit, said: "We are doing all we can to trace the driver of the vehicle.
"We would ask if anyone saw the vehicle around the time of the collision, or has seen it since, that they contact us.
"It may be the vehicle has been parked up and left somewhere nearby so I would ask people living in the area to check outside their house and call us if they see a vehicle matching the description."
An 11-year-old boy has been struck and killed by a car in Greater Manchester.