The five-year-old boy was seriously injured on Wednesday at Bunbury Museum and Heritage Centre in Western Australia.
He died two days later, police said in a statement on Tuesday.
The tragic incident happened during an environmental education school holiday program run by the Department of Biodiversity, Conservation and Attractions.
Paramedics were called to the scene about 10.30am and transported the boy in a critical condition to Bunbury Hospital.
He was later airlifted to Perth Children's Hospital.
City of Bunbury chief executive Alan Ferris said the council's staff were devastated by the incident and the museum would remain closed until Tuesday.
"Our entire organisation is heartbroken and deeply saddened to learn of the passing of the young child involved in a tragic incident," he said.
"Our thoughts are with the child's family, and everyone impacted."
Mr Ferris said support had been offered to the boy's family.
"There are no words that will help what we know will have an immense impact on our entire community," he said.
"We also send thoughts to our own staff who witnessed the incident and who did everything they could in providing immediate assistance."
The museum and heritage centre is operated by the City of Bunbury.
WorkSafe is investigating the incident and police will prepare a report for the coroner.
The city and the Department of Biodiversity, Conservation and Attractions are working with investigators.
Port city Bunbury is about 175km south of Perth and has a population around 33,000.
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