The youngster was crossing Queensferry Terrace, Edinburgh, at about 8:10am yesterday when he was hit by a blue car.
He fell to the ground, but the motorist drove off northwards towards Queensferry Road, where the vehicle disappeared from view.
The boy was taken to Edinburgh Royal Infirmary, where he was treated for a suspected broken leg.
Lothian and Borders Police appealed for information from any witnesses.
A force spokesman said: “This schoolboy sustained a serious injury as a result of this collision, and it is vital we trace the driver of the vehicle to establish the full circumstances surrounding this incident.
“We would ask that they make contact with police immediately.
“The area around Queensferry Road and Queensferry Terrace would have been busy at the time with parents dropping their children off at nearby schools. Anyone who may have witnessed the collision is also asked to get in touch.”
The vehicle was a blue car of medium size.