Hants Road Policing tweeted two photos of the vehicle which had crashed on the A34, just north of Winchester.
It came after heavy rain fell across the county with thunder, lightning and hailstorms in some areas.
Police officers, fire crews, paramedics and an air ambulance were called out following the crash.
Woman, 44, whose large Dobermann dog mauled girl, 3, on Leigh Park street released back into neighbourhood by police
Plans for redevelopment of Knight and Lee in Southsea get the green light - and work will begin soon, vows developer That Group
WATCH: This is the moment a man with a grudge fire-bombed a family's garden in Leigh Park
'It was just sheer panic from everyone': 'Horrific' bedroom fire in Paulsgrove ripped across several house roofs with 'pouring' smoke being seen from the motorway
Unidentified woman’s body found in water as Hampshire police investigate ‘unexplained’ death
In the tweet police said the driver was fine and had been treated at hospital.
The photos showed how the vehicle had come off the road and crashed into a tree.