The incident occurred on the slip road at Junction 11 at around 8.50pm on 26 December.
A 61-year-old man, a 48-year-old woman and two children were in the vehicle when the collision took place.
The boy, aged 11, was taken to Southampton General Hospital where he later died,
The driver, a 61-year-old man, suffered serious, potentially life changing injuries, the force said.
He is also being treated in Southampton General Hospital with the woman and the girl, aged nine, who suffered minor injuries.
The family are currently being supported by specialist officers, Hampshire Police said.
The force have appealed for any information about the incident to understand what happened.
Inspector Andy Storey, said: “We know the family were travelling from the Basingstoke area so we’d like to appeal to anyone who may have been travelling along this stretch of the motorway prior to the collision, who may have seen the vehicle, to get in touch with us.
“We would also like to speak to anyone who witnessed the collision. Did you see what happened? Do you have dash cam footage showing the collision or the moments beforehand?
“Please contact us on 101 or report online, quoting Operation Nomic reference number 44210516070.”
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