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.”
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Albion Street was closed in both directions while emergency services were sent to the crash.
The road has now reopened.