They say emergency services attended around 11.15 pm at a well-developed blaze at Carnsalloch House, a Grade A listed house and former charity-run home.
A joint Police Scotland and Scottish Fire and Rescue Service investigation has been launched into outbreak which caused extensive damage.
Detective Inspector Bryan Lee, Dumfries CID, is appealing for information.
He said: “Carnsalloch House is an isolated property to the east of Kirkton which has been unoccupied for some time.
“However, I am aware that local youths frequent the grounds of the property and there is information that in the past homeless people may have sheltered there.
“There is no information that anyone was sheltering within the house at the time of the fire, however, due to the condition of the building, neither the fire service nor the police are able to get access.
“As such, I am keen to speak to anyone who has recently been in or around the property or has any information that may assist the police with their enquiries.”
Anyone who can help is asked to contact police on the 101 non-emergency telephone number.