The man was involved in a collision in Vicar Lane shortly before 1.20pm.
Police closed the road in both directions while emergency services worked at the scene.
A spokesman said the man had been taken to Leeds General Infirmary for treatment but his injuries were not believed to be life-threatening.
He said officers were in the process of reopening the road.
First Bus had been diverting its southbound services via Eastgate, St Peters Street, Duke Street and Kirkgate.
Northbound services were diverting via Duncan Street, York Street, St.Peter’s Street and Eastgate.