Emergency services were called to the junction of St Peter's Street and York Street at 9.45am.
A single decker bus and a Toyota Auris had crashed, causing significant tailbacks on surrounding roads.
First Bus also diverted a number of services as a result of the collision.
A West Yorkshire Police spokesman said the driver of the bus had been taken to Leeds General Infirmary for treatment.
The crash came 20 minutes after another collision on Kirkgate, close to Leeds Minster.
Police said damage was caused to vehicles involved, but nobody was injured.