It happened at about noon on Albion Street, between The Headrow and Great George Street junctions.
A spokesperson for West Yorkshire Police said: “Police received a report of a road traffic collision in Albion Street involving a woman pedestrian and a bus.
“The woman, who is in her twenties, was taken to hospital for treatment to injuries that are not considered life threatening.”
Albion Street was closed in both directions while emergency services were sent to the crash.
The road has now reopened.