The blaze caused extensive damage to an unoccupied wing of the landmark 18th-century building.
Gardai at Gurranebraher station are handling the investigation.
Five units of the Cork city fire service raced to the scene on Wednesday night having received a call at 10.20pm.
A three-storey section of the building was destroyed in the inferno, as the roof collapsed.
The empty building has been the scene of anti-social behaviour including drinking in recent years.