Strathclyde Fire and Rescue were called out to the derelict St Mark’s primary school in the east end of Glasgow at 2.15pm yesterday.
Properties were evacuated near the fire in Muiryfauld Drive in Tollcross as a precaution and advised other residents to stay indoors because of thick smoke in the area.
There were no injuries.
A spokesman for the fire service said asbestos was found in the building but air-quality checks found no immediate risk to local residents.
Detective Sergeant Roland Craig said: “It has now been established that this fire was wilful and the building will have to be demolished. It will remain unsafe until demolition has been carried out.”
Police are appealing for witnesses to come forward.
“I am anxious to speak to anyone who was in the area around 2pm yesterday afternoon and saw anything suspicious to come forward,” said Det Sgt. Craig.
Mr Craig said officers want to speak to three boys who were seen at the school when the fire started. One of them was wearing an orange top and another wore a white, hooded jumper.