Thames Valley Police, in a statement on Tuesday night, said the collision took place on the northbound carriageway between junctions 14 and 15, near Milton Keynes, at around 11.10pm on Monday.
The two children, aged four and 10, were passengers in a white Vauxhall Astra which was in collision with a Scania HGV.
Their next of kin have been informed and are being supported by specially trained officers.
Another child passenger and the driver of the Astra were taken to hospital with injuries but have since been discharged.
The driver of the HGV was not injured.
Police are appealing for any witnesses to the incident.
A 35-year-old woman, from Derby, has been arrested on suspicion of causing death by dangerous driving and driving a motor vehicle when above the prescribed limit of alcohol.
She remains in custody.