New Zealand Prime Minister Jacinda Ardern has given birth to her first child, a girl weighing 3.31 kg (7.3 lb).

Ms Ardern, 37, became New Zealand's youngest prime minister when she took office through a coalition deal last year after an inconclusive election.

She now becomes the first woman in the country's history to give birth while in office.

"Welcome to our village wee one," Ms Ardern wrote on Instagram.

"Feeling very lucky to have a healthy baby girl that arrived at 4.45pm weighing 3.31 kg (7.3 lb) ... We're all doing really well thanks to the wonderful team at Auckland City Hospital."

She posted a picture of herself, smiling and holding the baby in a blanket, with her partner, television presenter Clarke Gayford.

Deputy Prime Minister Winston Peters has stepped in as acting prime minister and will run the country for the next six weeks while Ms Ardern takes maternity leave, according to an agreement they published earlier.

Ms Ardern is one of the few elected leaders to hold office while pregnant. Pakistan's Benazir Bhutto gave birth while she was prime minister in 1990.

New Zealand has long had a progressive reputation and was the first country to give women the right to vote in 1893 and Ms Ardern is the country's third female prime minister.

Ms Ardern has said she plans to return to work at the beginning of August.

Mr Gayford will take care of the baby and will travel with Ms Ardern between their Auckland home and the capital, Wellington, as well on international engagements.

Ms Ardern, who refused to discuss plans for motherhood during the election campaign, waited until January to reveal on Facebook she had conceived and was going to be "prime minister and a mum".

Her plans for a family had sparked a sexism row during the election when a television host quizzed her on the issue, saying voters had a right to know before they cast their ballots.

She rejected the line of questioning as "unacceptable", saying pregnancy and child rearing should not hinder women's opportunities in the workplace.

"It is a woman's decision about when they choose to have children and it should not predetermine whether or not they are given a job or have job opportunities," she said then.