Ms Ardern arrived at the country's largest public hospital at 5:50am (local time) on Thursday with partner Clarke Gayford, her spokesman said.
Noting there are "a whole lot of factors which we aren't aware of", she says it really could be anytime.
The Prime Minister's office confirmed Ms Ardern had entered hospital in a statement today.
Although she will become the first elected world leader to take maternity leave - and only the second to have a child while in office - Ms Ardern has played down the significant global attention she's received as a role model.
Yesterday Mr Gayford shared a photo of Ms Ardern at home reading, three days after the baby was due.
"I am able to do what I'm doing because I have enormous support around me and it makes me quite privileged".
Deputy Prime Minister Winston Peters is now Acting Prime Minister.
She's expected to briefly speak to reporters after the birth.
Ardern has said she is confident the government will continue to run smoothly in her absence.
Ms Ardern addresses parliament in Wellington.
Shaw was referring to the fact this will be the first time a Prime Minister in New Zealand has had a baby while in power.
The only other comparable example was Pakistan's Benazir Bhutto giving birth to daughter Bakhtawar while in office, on January, 25 1990.
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Children who struggle to contain their behaviour at that age in turn have fewer social skills and do worse in school at ten. The researchers from the study asked the parents and children to play as if they were home for their observations.
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