Ardern, who announced her pregnancy in January, is only the second world leader to give birth while in office after Pakistan's Benazir Bhutto, who had her daughter in 1990.
Ardern will leave her home town of Auckland to return to the capital, Wellington, on Saturday.
Although New Zealand law permits infants to be taken into the parliamentary chamber, Ardern told reporters she did not believe it would be necessary, nor did she intend to bring Neve with her to make a statement.
Prime Minister Jacinda Ardern says she is acutely aware of the example she is setting for other parents returning to work, and is clear that she is not going to pretend she is superhuman.
"Ultimately though, that first week back, I am going to be focused on getting straight back into it".
On Thursday, the 38-year-old spoke to press at her Sandringham house where she covered everything from mother's guilt, her new bub's digestive system and adjusting to her new sleeping routine.
Most New Zealanders did not know what to expect from the controversial figure, who ensured that Ardern's Labour party won last year's general election when he and his New Zealand First party threw their support behind a centre-left coalition. "Hope Neve enjoys her new portfolio of Minister of Cute".
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In an interview with The Associated Press, Ardern also said New Zealand was among many nations concerned about where a tit-for-tat trade war between China and the USA might lead, and that the notion of New Zealand becoming a republic was not a priority for her government.
"I absolutely accept this layer of interest because it's not our normal yet. I don't think anybody needs that". However, Ardern said the family will travel together to official engagements, including to NY in September, where she will make a speech to the United Nations.
Ms Ardern said so far parenthood has been fantastic.
"I'm multitasking like every single parent I've ever met, so a big shout-out to all of them", she said in the video, which has been praised by thousands of viewers.
She said her vision for the country was for it to live up to how peopled viewed it.
"All of the things that people said that I would experience - that idea that you suddenly have this new person in your life that you could love so much and that time will go incredibly quickly, but that the nights will seem incredibly long - all of that has been true, but it has been wonderful".
"I also have the ability to have [Neve] with me [at work] so that means that I'm privileged and I'm lucky".