The crash, in Harehills last night (August 21), is being investigated by West Yorkshire Police who confirmed that the black and white cab left the scene without stopping.
Officers were called to Foundry Approach shortly after 9pm by the ambulance service.
The 19-year-old was found with serious injuries after the collision at the junction with Bellbrooke Avenue. He was taken to Leeds General Infirmary and is currently being treated in hospital, where he is in a stable condition.
Enquiries are continuing to trace the driver of the taxi, which was described as a black and white people carrier type vehicle. It will have significant damage to the windscreen.
Anyone who witnessed the collision or the circumstances leading up to it, or who has any information that could assist the investigation, is asked to contact West Yorkshire Police’s Roads Policing Unit via 101 quoting reference 13230466795 or via the Live Chat website.