The incident, which has left residents in shock, was this week slammed by a leading community representative.
A police spokesman confirmed: "Pieces of burnt paper were discovered at the grocers shop in Whithorn on Sunday afternoon or through Sunday night.
"It appears they were lit and pushed through the letterbox of the property. We would like to speak to anyone who witnessed any suspicious behaviour in the area around the time of the incident and also remind people of the dangers associated with fire."
Mid Galloway Councillor Alistair Geddes hit out: "I think this is absolutely shocking.
"This is a business in Whithorn employing people who would have been out of a job if that shop had burned down.
"Also, on one side you have an elderly lady and on the other the Old Town Hall, so the consequences don't bear thinking about.
"If anyone has any knowledge of this incident they need to report it to the police. These people need to be identified."
No one was hurt in the incident and no damage was caused.