Police said it happened on the London-bound carriageway near Hollingbourne, Maidstone, around 6.41pm on Saturday.
There was “thick fog” in the area at the time, according to National Highways, and the motorway remains closed in both directions between junctions 8 and 9.
Three fire engines and a technical rescue unit were sent to the scene, said Kent Fire and Rescue Service.
Eleven people were passed to paramedics for treatment and police said two of them were seriously injured and taken to hospital.
Drivers posting on the Kent Traffic and Travel Facebook page said conditions around the time of the crash were hazardous.
“I drove through about half 6,” said Rob Rattenbury.
“The fog just appeared and was very thick. All cars were slowing down to about 30mph. Be careful out there.”
Ema Louise posted: “I was on the other side of the road and heard a massive bang but didn’t see anything as it was so foggy.”
Some users suggested that smoke from a nearby fireworks display may have made the visibility worse.
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The stretch of motorway affected remained closed in both directions shortly after midnight. Diversions are in place but motorists have been told to avoid the area.
Another Met Office warning for fog is in place until 10am on Sunday and covers a large part of southern England and the Midlands.
