At about 5 am on May 7 a blue-coloured Honda Civic car was found on fire in Carrick Road in the town.
The Fire and Rescue Service attended and extinguished the fire however the car was extensively damaged.
PC Victoria Urwin at Dumfries said: “The circumstances surrounding this fire are suspicious and we are seeking the help of the public to help us catch those responsible.
“Anyone who has any information which might help us should call us at Dumfries on 101.”