It happened at around 11am today (Tuesday) on the A653 Leeds Road, near the Babes in The Wood pub.
West Yorkshire Fire and Rescue Service said on Twitter that the woman was freed by fire crews before being taken to hospital.
Buses serving Dewsbury, Morley, Wakefield, Huddersfield and Pudsey have been disrupted after the incident.
Crews from Dewsbury and Morley were called to the scene.
The fire service said the crash only involved one vehicle.
And bus services around the area are now being affected after the crash.
Metro said that Arriva’s 117, 202, 203, 205 and 212 service are all affected.