The Northern Ireland Fire and Rescue Service was called to Holy Child Primary School at 21:20 GMT.
A spokesperson said that when crews arrived, the roof of the building in Central Drive, Creggan, was alight.
In a statement a PSNI spokesman said: “Police are appealing for witnesses following a fire at a primary school in the Central Drive area of Derry/Londonderry last night, Monday 04 April.
“At around 9.25pm police received a report of a fire at the school. Police and NIFRS attended and it was established that a fire had been started on the roof of a classroom at the school.
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“NIFRS extinguished the fire. Damage was caused to scaffolding and building materials as a result of the fire.
“Some damage was also caused to the school as a result of the incident.”
Inspector David Anderson is appealing for anyone who witnessed the incident or anyone who has any information that can assist with the investigation to contact officers in Strand Road on 101. Or, if someone would prefer to provide information without giving their details they can contact the independent charity Crimestoppers and speak to them anonymously on 0800 555 111.