The smash happened on the southbound carriageway between junctions 19 (Knutsford) and 18 (Middlewich) just before 7am.
Firefighters used cutting equipment to remove the doors of the car before rescuing four people.
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The driver of the Renault, a man, has been taken to hospital.
The extent of his injuries are not yet known, police said.
Two male passengers also sustained "minor injuries" and were taken to hospital as a precaution.
A spokesman for Knutsford Fire Station said: "This morning we were mobilised to a road traffic collision on the M6 between J19 -J18 Southbound.
"Five fire engines, police and ambulance crews attended the scene.
"The four casualties involved escaped with minor injuries and three were taken to hospital for further treatment."
Images released by the fire service show the Renault was completely destroyed in the crash.
One photo also shows a tree which had fallen onto the carriageway due to the impact of the HGV.
Two lanes remain shut following the collision, with Highways England reporting tailbacks of 10 miles and 90 minute delays.
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