Five plastic rubbish tins were set alight some time over the weekend.
Some were set up against brick buildings but one was placed less than 30cm away from the base of the wooden block.
Constable Brian McKinney, of Milton, said the heat from the fire was very intense because part of the building was scalded by flames and some paint began peeling off.
"This building could have easily gone up. That's how serious this was," he said yesterday.
The block of classrooms contains several rooms and forms an integral part of the school's facilities.
Const McKinney said the potential for major destruction may not have been realised by those responsible but any attempt to set fires was serious.
It was unclear when the fires were started but evidence of them was discovered by school staff yesterday morning, with the remains of the burnt bins scattered around the school.
