All of those who died were travelling in the minibus, which was from the Nottingham area.
A five-year-old girl, a woman, and a man are being treated in hospital with life-threatening injuries, while another woman has serious injuries.
The two lorry drivers have been arrested, one of them on suspicion of driving while over the alcohol limit.
Both men are being questioned on suspicion of causing death by dangerous driving and are in police custody.
The crash happened on the southbound M1 at Newport Pagnell in Buckinghamshire just before 03:15 BST.
South Central Ambulance Service said those injured in the collision were taken to hospitals in Milton Keynes, Coventry, and Birmingham.
Police said some of those involved in the collision were visiting the UK from India.
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.
Thames Valley Police said the two lorry drivers, one aged 31 and from Worcestershire, the other aged 53 from Stoke-on-Trent, were being questioned.
The 31-year-old man was detained on suspicion of one count of causing death by dangerous driving and one count of driving a motor vehicle when above the legal alcohol limit.
Pictures appear to show extensive damage to the lorries involved - a FedEx vehicle and one belonging to AIM Logistics.