Firefighters were called to help free the man after the incident near Junction 32 at Castleford, at around 3.30pm yesterday.
Motorists faced heavy delays as the stretch of the M62 between Junction 32 and 33 at Ferrybridge was shut in both directions while the Yorkshire Air Ambulance also attended the scene.
Crews from Castleford, Normanton and Wakefield fire stations freed the man after about 30 minutes and he was taken to hospital.
A Castleford Fire Station spokesperson said the driver of the other vehicle was not injured.
He said the air ambulance was not needed and left the scene.
The incident caused rush hour disruption for commuters and the M62 reopened in one direction at around 4.15pm.
But Highways England said the other direction did not fully reopen to all three lanes until around 6pm.
West Yorkshire Fire and Rescue Service said in a statement: “2 vehicles involved in road traffic collision. 1 male casualty was trapped and extricated by Fire Service personnel and transported to hospital by ambulance.
“Appliances from Castleford, Normanton and Wakefield stations attended the incident.”