The four girls, who were delivered via caesarean section at 28 weeks and four days on 14 July, were monozygotic quadruplets - where a single fertilised egg splits into four embryos.
The hospital said the girls' mother, 34-year-old Jenitar Na'amoana, and her husband Jortham, already had four children and were taken by "immense surprise" when told to expect quadruplets.
Dr Alexa Bendall, who cared for the mother from the start of her pregnancy, estimated identical quadruplets occur "at one in every 15 million pregnancies" and said "but to share the same placenta - this is unheard of".
Bendall, who is a maternal foetal medicine specialist and obstetrician, said such a pregnancy was very high-risk, with the hospital admitting Na'amoana as an inpatient at 25 weeks so she could be monitored.
