The days-old creature, which is also known as a chimaera, was discovered shortly after being hatched at a depth of about 1.2km (0.7 miles) on the Chatham Rise, an area of ocean floor.
Scientists from the National Institute of Water and Atmospheric Research said the deep-water shark must have recently been born as its belly was still full of egg yolk.
The embryos of ghost sharks develop in egg capsules laid on the sea floor and feed off a yolk until they become ready to hatch.
The team was carrying out a trawl survey to estimate populations of hoki fish when they discovered the neonate (newly-hatched) animal, which is related to sharks and rays.
Other names for it include rat fish, spook fish and rabbit fish, according to the Shark Trust.
Dr Brit Finucci, a member of the team, said of the very rare find: "It's quite astonishing. Most deep-water ghost sharks are known adult specimens; neonates are infrequently reported so we know very little about them." (www.news.sky.com)