The collision happened between Junction 15 for Stoke-on-Trent and Junction 16 for Newcastle-under-Lyme at 10.30am on Thursday but led to delays stretching back to Junction 14 for Stafford.
It happened on the northbound side of the carriageway, with one of the vehicles crashing through the central reservation.
The West Midlands Ambulance Service said the car driver, a man, has sustained non-life threatening injuries and received treatment on scene before being taken to Royal Stoke University Hospital for further checks. Both lorry drivers were uninjured.
The northbound section of the motorway remained closed as police and other emergency services tackled the incident and was expected to remain shut throughout the afternoon.
One lane was opened on the southbound side of the road, with drivers being urged to find alternative routes.
A spokeswoman for the West Midlands Ambulance Service said: "(We were) called at 10.25am to reports of a car and two lorry RTC on the northbound carriageway of the M6 between J15 and J16.
"An ambulance and paramedic officer attended and assessed the driver of each vehicle involved. The car driver, a man, sustained non-life threatening injuries and received treatment on scene before being taken to Royal Stoke University Hospital for further checks. The lorry drivers were uninjured."
The agency estimated there were delays of around 60 minutes prior to the closure, stretching back to Junction 14 for Stafford.
National Highways duty operations manager for the West Midlands, Rady Salim, said: “We’re working closely with police colleagues while they carry out work on scene and we’d encourage motorists to leave additional time for their journeys.”
Traffic travelling north was being diverted off at junction 15 northbound, following the A500 around Stoke back towards the M6. Traffic was then rejoining the M6 at junction 16.