To avoid scalpers, promoters say tickets for the show will be limited to two per person and no tickets will be distributed.
Ticket buyers will have to produce photo ID to pick up their tickets from the venue from noon on the day of the show.
Prince will also perform four shows at Melbourne State Theatre on February 16 and 17, two shows at the Sydney Opera House on February 20 and two shows at Sydney State Theatre on February 21.
The 57-year-old best known for hits like Kiss, When Doves Cry, and Let's Go Crazy is bringing his Piano and a Microphone tour, a solo show he had planned to take around Europe late last year but cancelled after the Paris terror attacks.
As the tour name suggests, Prince will perform alone on stage at the piano - fans will be out of luck if they want to dance to his funk-powered hits or wave a cellphone to the extended guitar solo of Purple Rain.
Ahead of the scrapped European tour dates, Prince said he planned the solo shows as a personal challenge.
"Why do this now? For several reasons. For starters it is a challenge. I rarely get bad reviews because this is something that's been perfected for over 30 years," he said at a press conference at his Paisley Park studio when he announced the tour.
"You have to try new things. With the piano it is more naked, more pure. You can see exactly what you get."
Prince played his first solo shows last month at his Paisley Park complex in hometown Minnesota, and received rave reviews.
Prince remains one of pop's enduring and enigmatic stars, as respected now for his musicianship and vast body of work as he was celebrated for his hits at his 1980s commercial peak.
It is estimated he has sold more than 100 million albums and he's won multiple Grammys, an Oscar and a Golden Globe.
Albums like 1999 (1982), Sign o' the Times (1987) and Purple Rain (1984) are considered classics.
On those - and some other 40 studio albums in his career - the multi-instrumentalist combined guitar rock, funk, soul, jazz, R&B, psychedelia and often sexually charged lyrics into a singular sound.
Prince's intimate Auckland show sneaks in ahead of two nights at Vector Arena in early March by Madonna - another other 80s pop icon to have never made it to New Zealand.
