The tree is blocking both Heights Way and Albany Terrace.
First Bus confirmed that the 15 service is diverting in both directions.
The bus company said: "Heights Way/Albany Terrace is blocked due to a fallen tree.
"Services 15 are diverting via Wortley Road, Whingate, Tong Road, Pudsey Road and Greenthorpe Road in both directions.
"We are sorry for any inconvenience caused."
It comes as the M1 is closed northbound between Wakefield and Morley due to two overturned lorries, while a flight originally bound for Leeds Bradford Airport from Lanzarote has been forced to divert due to strong winds.
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