The police, after their initial investigations, would not reveal any details, but said they were treating it as an accident.
Aryan was resuscitated and taken to Hawkes Bay Hospital. He was later put into a coma and flown to the Starship children's hospital in Auckland where he remained until he was returned to his local hospital several weeks ago.
He had suffered brain damage from the accident and his father, Anjan Banerjee, a doctor, spoke last month of his son's breathing difficulties and other ongoing complications.
Dr Banerjee also spoke of the shock of learning of Aryan's accident.
"I was finishing a clinic when I got a call from my wife saying Aryan had been badly hurt - I thought he had just fallen off the monkey-bars."
Dr Banerjee said he was spoken to by the principal, Marty Hantz, upon arriving at the school.
"He explained the situation, when I went over there I saw him there - they had just finished resuscitating and they were starting to intubate, that's not something you forget."
Mr Hantz could not be contacted this evening but said at the time of the accident that the school was working closely with the police and the Ministry of Education to work out what had happened.
Steve Alexander, chairman of the school's board of trustees, said this afternoon in a statement that Taradale Primary School received confirmation today that Aryan Banerjee had passed away.
"We extend our deepest sympathies to the Banerjee family," he said.
"Aryan has been in hospital since he was injured in an accident at school in May. He was a much loved member of our school. Our immediate priority is to support Aryan's family, and to focus on the wellbeing of all his friends and classmates, as well as the wider school community."
Mr Alexander said in the days ahead the school would be working with the Ministry of Education's support team, and would continue to provide details of grief counselling to the families of pupils.
"The WorkSafe NZ investigation into the May accident is continuing. The school will not be making any further comment until these investigations are complete."
When asked about what investigations it had made into Aryan's accident, the Ministry of Education said, "... Worksafe is the organisation with responsibility for any investigations into harm in the workplace".
" We know this is also a very difficult time for the staff and children at Taradale School and our thoughts are also with them," said Katrina Casey, the ministry's head of sector enablement and support.
"Since Aryan was seriously injured, we have been working to support the staff, students and board of trustees at the school. We know they've been deeply affected by what happened."
"We are very saddened to hear of the death of Aryan Banerjee and would like to express our deepest condolences to his family."