A Hampshire police spokesman said: "The road is expected to remain closed for the rest of the day while collision investigators examine the scene and arrange for the vehicle to be recovered."
More top news
Downpours keeping us on our toes today
The M20 in Kent has been closed in both directions after a pedestrian bridge allegedly collapsed on the motorway on Saturday.
The AA have warned of traffic jams and urged people to carry extra water in their vehicles because of the warm weather.