The crash happened on the eastbound carriageway near Micheldever‬, just after 07:30 BST.
A woman who was a passenger in the car was taken to hospital - her injuries are not thought to be life-threatening.
Highways England, which has replaced the Highways Agency, said the road reopened at about noon.
The road was closed eastbound from the A34 at Bullington and the M3 at North Waltham. Traffic was being diverted via the A34 towards Winchester.
Motorists were being advised to plan for longer journey times and find alternative routes.
The A303 was picked out by traffic information company Trafficmaster as one of the likely top five busiest roads over the Easter holiday period.
A driver died when his car left the road and overturned in a ditch on the A303 in Hampshire.