Officers were called to Undercliffe Lane at 2.06pm today after reports of a collision between a pedestrian - a man in his 70s - and the vehicle.
Firefighters and an ambulance also attended the scene after the man became "trapped" under the lorry near to the junction with Otley Road.
The man was treated by paramedics before being taken to Leeds General Infirmary.
His injuries are thought to be serious but not life threatening, West Yorkshire Police said.
A police cordon was in place and traffic was still disrupted at 5pm.
West Yorkshire Fire and Rescue Service said he had been "trapped under the vehicle".
Crews from Bradford and Shipley attended along with a Technical Rescue Unit from Cleckheaton