Police are investigating the circumstances surrounding the blaze in a lay-by at Burnhead Cottage near the village at about 11.12 pm on Tuesday night.
The fire was extinguished by fire crews, however the black coloured Vauxhall Insignia car was badly damaged.
And officers say subsequent examination indicates that it appears to have been a deliberate act. The car was parked in the lay-by, on the B722, at the time with one of the wheels removed to repair a puncture.
Constable Ryan McGarvey at Annan said: “We would like to hear from anyone who may have been using the B722 road between Annan and Eaglesfield late on Tuesday night.
“In particular, anyone seen in or around the lay-by at Burnhead Cottage we would be interested to hearing about. Callers can use the 101 number and give the reference number 0020 of 9/5.”