A West Yorkshire Police spokesperson said that a man aged in his twenties was injured but "conscious and breathing" after the collision at around 5.35pm on the A58 Roundhay Road in Harehills.
A driver had failed to stop after the incident, but it is not yet known what type of vehicle the person was using.
Gledhow Road was closed for some time - with traffic diverted to Roseville Road - but has since been reopened, police said.
Anyone who was a witness or who has information about the collision is asked to call 101.