Emergency services were called to Waiau Pā School in Pukekohe on Friday last week.
The child was flown to Auckland City Hospital in a critical condition.
Police said they were still in the early stages of their investigation.
St John said two ambulances, two rapid response units, an operations manager and a helicopter were sent to the school.
Ministry of Education acting hautū te tai raro Leisa Maddix said it was a "deeply distressing" time for students, staff and the wider school community.
"We are aware of the incident at the school and our traumatic incident team is actively supporting the school as needed.
"Our thoughts are with the child and their whānau during this incredibly difficult time."
RNZ has approached Waiau Pā School for comment.
