The fire, caused by an electrical fault in the engine compartment, destroyed the vehicle.
It caused traffic disruption on the bypass yesterday as the westbound lane had to be closed while emergency services worked at the scene.
Further recovery work also affected traffic flows.
A family, believed to include a young child, escaped unhurt and got to the safety of the roadside.
The vehicle was registered to a woman from Poole, police said.
Motorist Barbara Jackson and her daughter Vicky Millar were on their way back to Weymouth from Poole when they were caught up in the traffic.
Mrs Jackson said: “I have never seen anything like it; it was completely blackened out, a shell.”
She added: “We were in the hold- up for about 40 minutes and everyone was getting out of their cars and suddenly it started to move a bit and everyone went to the right-hand lane of the carriageway and we saw it on the left-hand lane completely blackened.”
She described seeing a young woman and a child on the side of the embankment and an elderly gentleman was helping them to retrieve their belongings.
Motorist Michael Davidson saw the car ablaze and then saw fire vehicles racing towards the scene.
He said: I saw there was a lot of smoke coming from down the road then I noticed the car. It was parked at the roadside just on the grass.
I saw a few flames from under the car and more smoke. When we got a bit closer I saw that the flames had engulfed nearly all of the front of the car.”
Dorset Police and the Highways Agency attended the fire towards the end of the bypass near Higher Bockhampton and placed a road closure on the westbound carriageway between Yellowham and Northbrook and traffic was diverted through Puddletown just after 11.30am.
Traffic could not get onto the bypass from the Troytown or at the Puddletown junctions.
The cause of the fire is believed to be an electrical fault, a spokesman for Dorset Fire and Rescue Service said.
He added: “We received calls at 11.30am from members of the public to the Puddletown bypass. A crew from Dorchester attended.
“Dorset Police closed one side of the road, the westbound carriageway.”
The carriageway was closed for just over twenty minutes as firefighters tackled the blaze using water jets.
No one was injured and the road was reopened just after 12noon.
Dorset Police said that recovery was arranged for the vehicle but it had to be allowed to cool down first.
The spokesman for Dorset Police added that the occupants of the vehicle were out of the vehicle ‘safe and well’ and were taken to Dorchester for onward travel.