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Emergency services were called to the blaze at East Gore Primary School shortly before 8pm.
The destroyed building was formerly a swimming pool and had been used as a storage and wet weather physical education facility..
Detective Sergeant Greg Baird, of Gore, said a scene examination indicated the fire was suspicious.
Several people, including school-aged children, had been seen in the school grounds in the time leading up to the fire.
Police were keen to speak with them to establish whether they had seen anything suspicious.
Anyone with information should call Gore Police on 03 203 9300. Information can also be provided anonymously to Crimestoppers, on 0800 555 111.