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The incident occurred on June 30 at Latham Park. It was reported to the council on July 3.
Council parks manager Lisa Wheeler said the accident occurred when a child was playing on a piece of equipment that consisted of a mound with concrete tunnels through it, topped with a fort and slide.
The boy, aged 3, was crouched above the entrance to the tunnels that sits on top of the mound.
He lost his balance and fell into the concrete tunnel, hitting his head, she said.
The boy sustained a concussion and bruising.
Council staff had been in touch with the boy's mother after she informed them of the incident. The opening he had fallen through had been temporarily boarded up.
The piece of equipment had not been the site of any previous accidents since it was installed in 2007, Ms Wheeler said.
The equipment had been audited recently and no issue had been raised.
Since the incident, the council had returned to the auditor to seek further advice on whether anything needed to be done with the equipment.
There had not been a large number of playground accidents reported to the Parks Department, Ms Wheeler said.