Firefighters say most of the windows on one side of the ground floor of Willow Park School were broken when they arrived at the two-storey building in the city's southeast.
Crews later found rocks on some classroom floors, but it's not yet clear whether the fire was deliberately set.
Police have taped off much of the school grounds in their search for clues.
There were no injuries and parents are being asked to watch the Calgary Board of Education website for information on when classes will resume.
More than 600 students attend Willow Park, which offers an arts-centred program for grades 5 through 9.
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