The vehicles were all travelling in the same direction between junctions 15 and 14, police said.
Buckinghamshire and Milton Keynes Fire and Rescue Service said it had sent six crews as well as three search and rescue vehicles to the scene.
Firefighters used hydraulic equipment to release three people from a vehicle, who were taken to hospital with a fourth person.
Highways England said traffic trapped between junctions 15 and 14 was being released past the scene, and diversion routes were in place from junction 15, with traffic following the A508, A5 and A509 to rejoin the M1 at junction 14.
Northamptonshire Police have asked people travelling to the British Moto GP at Silverstone to allow more time for their journey.
Ch Insp Henry Parsons, of Thames Valley Police, said: “Emergency services are continuing to work at the scene and road closures remain in place.
“We are aware there are a number of large scale events taking place this weekend and this closure is likely to have a significant impact on traffic disruption, so please allow extra time for your journeys.”
The M1 is expected to be one of the country’s busiest roads over the Bank Holiday weekend.