She said the baby arrived at 4:45pm (local time), weighing 3.31kg.
I think we are really privileged in New Zealand to have a prime minister who is going to know what that's like.
The 37-year-old took to Instagram to reveal the birth of her daughter Thursday (Jun 21), but has downplayed the significance of her pregnancy.
Since being elected, Ms Ardern has become an global political figure and there will be intense interest in the Prime Ministerial baby.
Ardern, who in October became New Zealand's youngest prime minister in more than a century, drew worldwide attention in January when she announced she was pregnant with her first child.
She added that both mother and daughter were doing well.
Ardern announced the birth on Facebook. At the time, she said she'd found out about the pregnancy just one week before her Labour Party formed government and that it came as a surprise to her, and her partner, as they believed they would not be able to conceive naturally.
New Zealand resident Jenni Werth, who is pregnant, told The Guardian that she is "intrigued with how much of a difference [the pregnancy] might make in her understanding of what it's like to be a working mum - and she's obviously at one extreme of the spectrum".
Analysis:Jacinda Ardern has arrived at hospital to have her baby and Winston Peters is in charge of the country.
She thanked everyone for their kindness and wishes.
Winston Peters, New Zealand's deputy prime minister, has taken over in the meantime, and Ardern is planning to take a six-week leave before returning, the AP reported.
"It is a woman's decision about when they choose to have children and it should not predetermine whether or not they are given a job or have job opportunities", she said then.
Ardern worked until late into her pregnancy, regularly encountering members of the public who touched her stomach and passed on gifts such as "onesies" and miniature rain boots, known as "gumboots".