Shortly before 9 pm on Monday, Police Scotland and the Scottish Fire and Rescue Service were called to Annandale Distillery following reports of a blaze.
The flames were quickly extinguished, but police say that it appeared to have been some form of bin that was set alight deliberately.
Sergeant Scott McDowall at Annan confirmed that there have been several reports of youths congregating in the area and setting fires.
And he said: “There have been reports of several deliberate fires in the area recently, requiring the attendance of both SFRS and Police Scotland, particularly in the area of the distillery and nearby riverside.
“Fire can spread quickly and as a result become dangerous, increasing the risk to property and people, including those setting the fires and causing concern to those living nearby.
“I would urge parents to speak with their children and remind them of the dangers of fire-raising.”
Anyone with any information on incidents of fire-raising should contact Police Scotland on 101.