The 37-year-old Ardern is set to become just the second elected world leader in modern times to give birth while in office.
Ms Ardern's due date was June 17.
The birth has been highly anticipated in the South Pacific nation of nearly five million people.
She has not said whether she is expecting a boy or a girl.
Ms Ardern's office confirmed she had arrived at the hospital with partner Clarke Gayford.
Deputy prime minister Winston Peters has taken over as acting prime minister.
Ms Ardern plans to take a six-week leave before returning to work.
Under the arrangement, Ms Ardern will still be consulted on major decisions, including issues of national security.
Ms Ardern has said she is confident the government will continue to run smoothly in her absence.
She said she hoped to be "sharing the good news" in an announcement but also to have some quiet time to enjoy as a family.
Asked earlier this month how the couple had been faring while trying to choose a name, Ms Ardern responded: "Terribly. Do you have any suggestions?"