West Yorkshire Police were called to the outbound lane of the busy route, opposite Go Outdoors, just after 5.30pm yesterday (Friday).
The crash was between the quad biker and the driver of a small white van.
The quad bike rider, an 18-year-old man, was taken to Leeds General Infirmary.
His injuries are not believed to be life-threatening.
The eastbound road was closed for several hours while police conducted their enquiries.
People driving into Leeds also faced delays.
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