The car, which ended up on its side, may have been in collision with a white Mercedes Sprinter van moments earlier on the A338, said police.
Two male occupants of the green BMW 325i were taken to Poole Hospital with serious, but not life threatening, injuries. One has since been arrested and is helping officers with their inquiries.
Police are appealing for witnesses to the incident which happened at around 12.35am on Thursday morning.
The road was partially closed for several hours due to damage to a crash barrier but it has since been made safe by local authority workers and the road was fully open by 4.10am.
Anyone with information is asked to call PC1823 Stroud on 101.