The collision occurred at around 6am, causing one of the lorries to shed hundreds of water bottles onto the carriageway.
One of the drivers was rushed to hospital with "serious leg injuries" following the smash, police said.
Pictures from the scene show the bottles strewn across the road, with one of the lorries resting on the central reservation barrier.
Two lanes were also closed on the southbound carriageway as crews worked to remove the lorries, clear an oil spill and repair the central reservation barrier.
Both the southbound and northbound carriageway fully reopened at around 2.15pm.
"The northbound M6 at Carnforth in Cumbria has now reopened following this morning's incident," a spokesman for National Highways said.
Drivers planning to travel beyond Carnforth to Kendal, Penrith, Carlisle and Scotland were advised to use the diversion route or delay their journeys.
HGV drivers were also reminded that a low bridge - 16ft high at the centre of its arch and 12ft 3in at its edges - was located on the diversion route.
Cumbria Police, Lancashire Police, Cumbria Fire & Rescue, Lancashire Fire & Rescue, North West Ambulance Service and National Highways all attended the incident.
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