Police are now appealing for information over the crash, which happened on Foundry Lane in Seacroft at 5.15pm on Wednesday, November 24.
The boy was crossing the road from the direction of Foundry Mill Drive when he was hit by a black car, which approached from the direction of the A64.
He ran to the pavement but fell and left his leg trailing in the road. The car then drove over his leg and failed to stop.
West Yorkshire Police has said the car has been described as a 'family-type car'. After running over the boy's leg - causing the break - it increased its speed and drove off, police said.
Anyone who witnessed the incident, or has any information that could assist in the force's investigation, is asked to contact PC 404 Cullen at the Roads Policing Unit via 101 quoting reference 13210612894 or online here.