Deputy Prime Minister Winston Peters was now acting prime minister and would run the country for the next six weeks while Ardern took maternity leave according to a previously published agreement, her office said in a statement.
Ardern arrived at the country's largest public hospital at 5:50 am local time with her partner Clarke Gayford, her spokesman said.
Ardern, 37, took office as New Zealand's third female prime minister last year and announced in January that she was expecting a baby with Gayford, a television fishing show presenter.
Auckland District Hospital declined to comment.
Just a handful of elected leaders worldwide have given birth while in office, notably Benazir Bhutto, who had her son in 1990 while Prime Minister of Pakistan.
Peters - a colourful political veteran and head of the populist New Zealand First party - had already taken over some of Ardern's duties in recent days, including running cabinet meetings in the capital of Wellington while she stayed close to home in Auckland.
Ardern has said there would be little disruption during her time off as she would stay in regular contact with Peters and involved in major decisions.
Ardern has continued to work right up until the birth, with her partner posting on social media on Wednesday afternoon a photo of her poring over official documents from home with the hashtag "#stillwaiting".