Police are appealing for witnesses to the incident, which happened shortly after 1.50pm yesterday afternoon.
According to the force, officers tried to stop a dark grey Kia Sportage which was speeding on the eastbound carriageway.
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Shortly after passing the Rownhams Services slip road, the Kia collided with a white Volkswagen Golf, and both vehicles then hit a roadside barrier, coming to a halt.
The driver of the Volkswagen Golf was not injured.
Police arrested a 32-year-old man from Southampton on suspicion of dangerous driving and drink driving.
He has been released from police custody but remains under investigation while officers looking into the incident carry out their enquiries.
A spokesperson for the force said: “Investigating officers would like to hear from anyone who was travelling on the M27 at the time of the incident and saw the collision or the Kia Sportage in the moments beforehand.
“We are particularly keen to hear from anyone with dash cam footage that captured the incident or the Kia Sportage.”
Those with information can call 101 or make a report on the police website, quoting 44230354204.
As a result of the crash, lanes 1, 3 and 4 of the eastbound carriageway were closed while officers at the scene dealt with the incident.
This led to long delays, with county council-run traffic information service ROMANSE reporting tailbacks of up to 40 minutes at its peak.
By 5pm, the road was cleared.