The 13-year-old was struck by a vehicle on Old Run Road in Belle Isle shortly after 5pm yesterday.
She was today being treated in Leeds General Infirmary for injuries described as “serious but non-life threatening”.
The vehicle that hit the youngster failed to stop at the scene and is said to have been black in colour.
Police have received separate reports of a black Vauxhall Corsa - possibly a mark two model – being driven in an erratic manner in the area around the time of the incident, which happened near Old Run Road’s junction with West Grange Drive.
Anyone with information is asked to ring PC 6833 Harding of West Yorkshire Police’s eastern area safer roads and neighbourhood support team on 101.