The children got out of the centre in the Auckland suburb of Mt Eden on Thursday but were quickly found and returned safely by a past parent.
BestStart deputy chief executive Fiona Hughes said they acknowledged the very serious nature of the incident and immediately commenced an investigation.
"This investigation is currently ongoing. We have informed the Ministry of Education and will work closely with them."
Hughes said the centre had restricted access to the door while investigations were conducted and they would take action as soon as findings were complete to ensure this could not happen again.
BestStart had apologised to the parents of the children involved and to all parents who entrusted them with the care and safety of their children, she said.
"We have undertaken to advise parents of the outcome and the actions from the investigation."
