Last week, St John ambulance confirmed it had been alerted at 9.48am and a helicopter was used to transfer the child to Dunedin Hospital on July 27.
Gems director Gemma Smith said the team were ''deeply saddened this has happened".
"We do everything possible to provide a safe environment for the children we care for."
There were systems in place for "immediate assistance" when accidents occurred and she would fully co-operate with WorkSafe and the Ministry of Education, Smith said.
She would not give further information on what happened.
WorkSafe confirmed that an investigation had begun.
The Gems website said the services offered were child-led, with the curriculum "facilitated through a fun, outdoorsy, creative and committed team of educators".