The spokeswoman said the fire was contained to the shed.
Police have been notified and are making enquiries along with Fire & Emergency New Zealand.
A police spokeswoman confirmed there had not been any arrests related to the fire as of mid-morning on Monday.
Henry Hill School shared a post on social media about the incident on Sunday.
“Just letting you know that there has been a fire in our caretaker’s shed this morning.
“Luckily it was quickly contained and no one was hurt.
“Our classrooms and other school buildings are all good.
“Safety measures will be in place around the damaged area.”