Deputy Prime Minister Winston Peters has been made Acting Prime Minister and will run the country for the next six weeks while Ms Ardern takes maternity leave.
Ms Ardern took office as New Zealand's third female prime minister past year and announced in January she was expecting a baby with Gayford, a television fishing show presenter.
Marama Davidson, co-leader of the Greens, said: "I am thinking of Jacinda with so much excitement as she approaches giving birth for the first time".
"It's a happy day and on behalf of the coalition government we wish her and Clarke all the very best".
"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.
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Ardern gave birth in Auckland Hospital, the country's largest public hospital, with her partner, television presenter Clarke Gayford, at her side. The head of the populist New Zealand First party had already taken over some of Ardern's duties, including running cabinet meetings in Wellington while she stayed close to home in Auckland.
The popular prime minister revealed she found about the bub after a fight with Mr Gayford, who hosts a fishing documentary show aptly named Fish of the Day.
New Zealand's First Couple announced they were expecting their first child in January and said they were hoping for "a bit of quiet time together as a family" before fronting the media once the child was born.
"It makes a little bit more sense for me to be grounded in one place from now on", she said at the time.
Yesterday Clarke Gayford tweeted a photo of the prime minister still working at home.