"Feeling very lucky to have a healthy baby girl that arrived at 4:45 p.m. weighing 3.31 kg (7.3 lb)… We're all doing really well thanks to the wonderful team at Auckland City Hospital," Jacinda Ardern wrote on her Instagram page.
The prime minister shared a picture of herself, beaming and holding the baby in a woolen blanket, with her partner, television presenter Clarke Gayford.
While Ardern stayed close to home in Auckland during the last days of her pregnancy, Winston Peters, the head of populist New Zealand First party and deputy prime minister has performed the duties of the prime minister. Ardern will take a six-week leave before returning to work.
Prominent politicians have already congratulated the couple. New Zeland Minister of Justice, Courts, Treaty Negotiations Andrew Little has posted a video card on his Twitter page.
The US Ambassador to New Zealand has also congratulated the Prime Minister.
Twitter users also reacted to the happy occasion.
New Zealand Prime Minister Jacinda Ardern is the second world leader to give birth while holding office after late Pakistani Prime Minister Benazir Bhutto, who gave birth to daughter Bakhtawar in 1990.