Ardern found out she was pregnant on October 13, just six days before she was propelled into the job when Peters, the leader of the New Zealand First Party, announced he was siding with her Labour Party in post-election negotiations.
She wrote on social media at the time: "We'll be joining the many parents out there who wear two hats".
"Thank you so much for your best wishes and your kindness", Ardern, 37, added. However, there's been a lot of talk about her temporary replacement, Deputy Prime Minister Winston Peters, a highly experienced, but sometimes polarising figure.
Ardern and partner Clarke Gayford announced the arrival of the girl - the couple's first child together - who was born at 4:45pm local time at Auckland City Hospital.More news: Jay-Z, Beyonce Release Surprise Album 'Everything Is Love'
Hobbs explained on CNN how Ms Ardern has stepped down for the next six weeks, leaving Winston Peters is in charge of the country.
Ardern's due date was June 17.
The public has generally been supportive of the popular prime minister.
She is the first world leader to give birth in almost three decades.
"It was a defining moment, especially for young women, proving that a woman could work and have a baby in the highest and most challenging leadership positions".More news: England less threatening than Belgium, says Panama's Rodriguez
Realistically, Ms Ardern will be hoping for a smooth six weeks while she's away, and Mr Peters will not want to be remembered for a auto crash of a time. She will take six weeks of parental leave, returning to office in August.
Under the arrangement, Ms Ardern will still be consulted on major decisions, including issues of national security.
Ardern becomes only the second serving second prime minister in history to give birth.
Ardern is NZ Labour's youngest ever leader and the country's youngest PM since 1856.
The first female prime minister was Sirima Bandaranaike, who was elected to lead Sri Lanka (then Ceylon) in 1960.More news: Phil Mickelson under fire after hitting putt before it stopped rolling
Ardern's pregnancy was unexpected, she said in January. One group started a campaign, #KnitForJacinda, to knit baby clothes for hospitals and women's shelters in celebration of Ardern's news.