Ms Ardern broke news of the birth on social media, saying she felt very lucky and thanking staff at the hospital in Auckland.
In a statement, she also said:
"I'm sure we're going through all of the emotions new parents go through, but at the same time feeling so grateful for all the kindness and best wishes from so many people. Thank you.
Ms Ardern, who was elected in October, announced in January that she and her partner Clarke Gayford were expecting a baby.
"I am not the first woman to multitask. I am not the first woman to work and have a baby; there are many women who have done this before," she had said earlier this year in an interview with Radio New Zealand
She is the youngest prime minister the country has had since 1856.