The Early Childhood Council has advised childcare centres to take extra care with large trees following Tuesday's incident.
Council President Theresa Dodd said her first concerns were with the injured children and their families, the centre owners and teachers, as well as the non-injured children and their families.
"We wish everybody well, and we hope the children recover as quickly as possible."
Dodd said the accident was "very unexpected".
"I have never heard of it happening before at a New Zealand early childhood education centre."
The current regulations require childcare centres to check hazards daily, Dodd said.
"And we will be advising our members with large trees on their property to include these in this hazard management routine.
"If one looks sick, we will be recommending they seek the advice of an arborist."
Dodd said the ECC would be examining publicly-available documentation that investigated the causes of the accident, and would be making additional recommendations to its members based on this information.
ChildForum chief executive Dr Sarah Alexander told the Herald that the incident highlighted several key issues in the way childhood centres are regulated.
"This incident could, perhaps, lead to the Ministry of Education looking into what training owners and teachers have and whether trees are regularly checked by an expert in the care of trees - an arborist."
Discoveries Educare owner Arjit Singh told the Herald on Tuesday that there had been concerns over the tree since the daycare opened following renovations of a large villa three years ago.
They opened in autumn, but noticed the following spring the tree was not producing leaves.
He asked a "handyman" who had done work for the daycare to look at the tree.
The handyman told them the tree was not diseased.
Singh also raised concerns about the tree with the agent that managed the leased property on behalf of the landlord, however said he did not receive a response.
Singh said he should have had a professional look at the tree, however was never concerned the tree would fall over. He was only concerned it did not produce leaves.
"[It was] never in our dreams that such a thing would fall."
He said he planned to get other trees at the site checked by a professional.
"I will make sure that happens."
Steve Peace, Auckland Council's Manager Compliance - Resource Consents, said there weren't any records of any calls or complaints being made to the council regarding the tree in the last few years.
He said the council, at the direction of arborists, is only able to remove trees on private property if there is an imminent risk to safety. Trees on private property are the responsibility of the landowner.