Shortly before 1 am, the occupants of a house in Greenwell were awoken and observed their Mazda 6 on fire.
As a result of the fire, the Mazda 6 subsequently rolled down the hill striking a Toyota.
Fire crews attended and put out the blaze, which they say was deliberate.
Constable Douglas Black said: “We want to hear from anyone who may have been in the Dunscore area around 1 am this morning and has any information which might help us catch those responsible.
“Setting fire to property such as this is extremely reckless and the consequences could have been tragic had the fire spread to other vehicles or the nearby houses.”
Anyone with information should contact Sanquhar Police Office on 101 or Crimestoppers on 0800 555 111.