Airline Pacific Blue said the baby was only discovered an hour after the flight landed at 5:20am as one of its members of staff cleaned the toilet.
Meanwhile, the woman who disembarked was identified in the airport terminal because of her blooded clothes, local media reported.
She was taken by police to Auckland's Middlemore Hospital where she underwent surgery and was reunited with her baby, whose gender has not been revealed.
Incredibly, none of the 150 passengers or the air-stewards on the flight realised the woman going into labour.
However, the General Manager of the airline, Adrian Hamilton-Manns said, "It's a nice, in a strange way; it's a nice thing to happen.
"We feel a great connection with this little baby, so we've already been in touch with the Samoan High Commissioner in Auckland, we've extended all support we possibly can to bringing out relatives, to providing our support, and also to our staff as well."
Immigration officials are investigating what information the woman provided on her visa application and how she was able to board the airplane at such an advanced stage of pregnancy.
Adrian Hamilton-Manns insisted the airline had adhered to its procedures, saying: "Our processes were followed for that flight, where all people who were pregnant were actually asked about how far pregnant they were."
A spokesperson from the hospital said both mother and baby were doing well