The incident was reported to emergency services at around 2:10am yesterday, after a member of the public noticed flames coming from the gym building at Parkside Primary on Waterside Road.
No one was injured and the Scottish Fire and Rescue service quickly discovered the seat of the fire, which measured approximately 18 inches by 18 inches.
A school spokesperson said the fire “seems to have been confined to the roof of the gym hall” and that the samage was limited to the external area of the roof.
Divisional officers are now carrying out inquiries in an effort to trace those responsible and are eager to hear from anyone who noticed unusual or suspicious behaviour in the area around the time of this incident.
A small group of youths were seen in the vicinity of the school and officers are particularly keen to speak with them as part of their ongoing investigation.
Inspector Alistair Hutchens of Police Scotland said: “Fortunately no one was injured and this fire never had the opportunity to grow thanks to the actions of a member of the public and the quick response of the emergency services.
“However, this is a very serious matter and we are conducting various lines of inquiry in an effort to trace those responsible.
“We are looking very closely into the reports of a small group of youths who were seen in the area and I would urge anyone who can help us identify them to come forward immediately.”