They also damaged two parked vehicles, cracked security lights and sprayed a graffiti tag on the primary school's car park.
Caretaker Richard Moullin believed the shed was so badly damaged that it could not be repaired so the school would have to raise the money if it was to be replaced.
The incidents happened between 7pm on Wednesday and 6.30am the following morning.
Head teacher Cate Mason said she was aware of the incident, which took place during the half-term break.
'They gained access to the school grounds, but did not enter the building,' she said.
The site is secure, with hedges, fences and locked gates, and Mrs Mason said whoever did the damage must have scaled a fence to get in.
'This sort of incident is very rare,' she said.
