Her deputy Winston Peters is now acting prime minister, although Ardern will continue to be consulted on significant issues.
The baby arrived Thursday afternoon, weighing 3.3 kilogrammes (7.3 pounds).
New Zealand's Prime Minister Jacinda Arden has given birth to her first child, becoming only the second to do so while in office.
For the first time, this was done by Benazir Bhutto, the Prime Minister of Pakistan.
"Based on what I've heard so far she seems very alert - just like my daughter Isabella who is very excited to have a baby cousin", she said.
Ms Ardern gave birth to a healthy baby girl on Thursday, the first for her and partner Clarke Gayford.
The 37-year-old is regaining her strength with macaroni and cheese and plans to spend at least one more night in an Auckland public hospital with her newborn girl.
In an Instagram post, the NZ PM highlighted Libby's work, naming her as one of many people who assisted her during the birth.More news: Kansas guard Mykhailiuk selected by Los Angeles Lakers in NBA Draft
Laurell Ardern said she'd had people come up to her saying that her daughter had been an inspiration, including one woman who anxious a job was too hard for her, but then thought 'Well, if Jacinda can do it, I will do it'. "Thank you", Ms Ardern said. "We're all doing really well", she wrote.
Coincidentally, the baby was born on Ms Bhutto's birthday.
Ardern is scheduled to take six weeks of parental leave before assuming the office, after which her partner Clarke Gayford, a television presenter will become a stay-at-home parent. "I am not the first woman to work and have a baby; there are many women who have done this before".
The British Prime Minister Theresa May sent a lovely message, along with New Zealand MP Nikki Kaye and the Governor-General of New Zealand Patsy Reddy.
"This is a sign of our maturity as a country and its acceptance that combining career and family is a choice which women are free to make", Clark wrote in an email. A spokeswoman for the prime minister said Thursday that Gayford had driven Ardern to the hospital in the couple's own vehicle.
Clark, who left office in 2008, added that Gayford should be celebrated as "a modern man, who is happy to be the full time parent of a young child".
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.