Green Party politician Julie Anne Genter overnight announced the arrival of her first child, weighing nearly 4.3 kilograms (Nine pounds, eight ounces).

"We waited a very long time for labour to start, but when it did it was short and sharp," she said on social media, posting a photo of her baby and partner Peter Nunns.

Ms Genter, 38, gave birth at Auckland Hospital, the same unit where New Zealand Prime Minister Jacinda Ardern had daughter Neve in June.

"So pleased to hear of the safe arrival of the newest addition to the parliamentary play group," Ms Ardern tweeted on Wednesday morning.

"Hope you enjoy those very special first few days."

Ms Ardern last week returned to parliament following a six-week maternity leave. Ms Genter has flagged she'll be taking up to three months away.

Over the weekend, Ms Genter drew the attention of major publications around the world by announcing she had bicycled herself to the birthing unit to be induced, two weeks after her due date.

"My partner and I cycled because there wasn't enough room in the car for the support crew," she said.

Also the country's associate transport minister, American-born Ms Genter is a well-known and outspoken cycling advocate - her colleagues describing the bike trip as "very on-brand".

Before she left the capital, she told AAP there was a sense of hopefulness among women seeing government ministers becoming mothers for the first time

"I think that it's OK to celebrate it. I don't think we're at the point where we can say 'no big deal'," she said.

A playground is currently being built on New Zealand's parliament's grounds amid a push by the Speaker of the House to make the precinct more family friendly.

A child-care centre was established in the building in the 1990s and a room for breastfeeding was established near the debating chamber in 1983.

Australian Associated Press