The accident occurred on the southbound carriageway of the motorway at junction 45 at around 9.15am.
West Yorkshire Police said an Iveco Daily dropside pick-up lost part of its load on to the two lanes of the carriageway.
The driver of a Man heavy tractor artic slowed to avoid the she load, and a Iveco Eurocargo rigid lorry went into the back of this vehicle.
A police spokesperson said: “The male driver of the Iveco rigid lorry was initially trapped in his vehicle and had to be freed by West Yorkshire Fire and Rescue Service.
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“He was taken to Leeds General Infirmary where he is being treated for injuries which are not believed to be life threatening.
“Police are keen to speak to anyone who witnessed the collision or saw the load come off the back of the Iveco dropside pick-up. Anyone with information is asked to call the Eastern Area Safer Roads and Neighbourhood Support Team on 101.”
Highways England said initially that three lanes of the motorway between junctions 44 and 45 were closed, causing delays.
Disruption continued well into the afternoon while the vehicles and debris are removed from the carriageway.
Fire crews from Gipton and Rothwell, along with the Technical Rescue Unit from Cleckheaton, were able to release the driver from the lorry.