The single-vehicle smash took place at 4am on Saturday.
A silver Vauxhall Corsa left the carriageway at the Marchwood bypass, on the A326 towards Hythe.
Officers attended and the road was closed while the incident was dealt with.Five people were injured in the crash, with two of those suffering serious injuries, police said today.
Hampshire Constabulary has now launched a county-wide appeal for witnesses to the incident.
A spokesman for the force said: ‘We are keen to speak to anyone who may have witnessed the collision or who may have any information about the incident which assists our enquiries.
‘Officers particularly would like to hear from anyone who may have broken down or seen a broken down vehicle in the area in the 24 hours prior to the incident.’
Anyone with information should call 101, quoting the reference 44220028801.