The baby, weighing 3.31 kilograms (7 pounds 3 ounces), was delivered at 4:45 p.m. on Thursday at Auckland Hospital, Ardern's office said in a statement.
She also thanked everyone for their "best wishes and kindness".
Jennifer Curtin, a professor of politics at the University of Auckland, said there was symbolic importance in Ms Ardern giving birth as it showed political parties around the world that it was fine to have younger women as candidates. "My full congratulations go to both Jacinda and Clarke, and I wish them and their new baby all the best", Clark said.
Another outlet even put together a baby-themed playlist to "help bring her bub into the world".
A pregnant Ardern addressing the New Zealand Parliament in Wellington in May. I think we are really privileged in New Zealand to have a prime minister who is going to know what that's like.
However, the baby has a higher chance of being named Oliver or Jack - the two most common baby boy names of 2017.
Ardern's daughter came into the world on Thursday, 28 years after the late Bhutto's daughter Bakhtawar was born.
New Zealand's prime minister has arrived at the hospital to have her first child. She previously shot down questions about whether a Prime Minister can have a child in office and still continue her duties, telling a press conference she is not "the first woman to multi-task".
It was an extraordinary rise for Ms Ardern - she only became leader a few weeks before the September election when her colleagues turned to her to save them from an electoral massacre.
Marie Ardern, the prime minister's aunt, who lives in Taranaki, was in tears after hearing the news. "Plenty of women have multitasked before me, and I want to acknowledge that", she said when revealing the pregnancy in January.
"Of course, the fact I'm having a baby while in office is [unprecedented]".
But he'll still be limited by the decisions of the Labour Party-dominated cabinet. She led the group for three months before being elected Prime Minister. Her deputy, Winston Peters, is to run the country as acting PM for the next six weeks.