An initial “potential” warning was upgraded to a tsunami after a wave measuring 30 centimetres was generated near the sparsely populated East Cape about 90 minutes after the earthquake struck.
“The first tsunami activity has arrived. Tsunami activity will continue for several hours,” the Civil Defence organisation, responsible for national emergency management, said in a statement.
The warning covered the East Coast of the North Island and the upper South Island.
The shallow tremor was estimated at a depth of around 30 kilometres (18 miles) off the coast, according to the US Geological Survey.
It was centred 167 kilometres (103 miles) from the nearest main town, Gisborne, which has a population of around 45,000.
Radio New Zealand reported that residents in coastal areas of the East Cape region were being advised by local civil defence officials to evactuate.
Civil defence public information officer Sheridan Gundry said the emergency management centre has been activated.
The earthquake, which struck at 4:37am (1637 GMT) was felt over much of the country but there were no immediate reports of damage.
New Zealand is on the boundary of the Australian and Pacific tectonic plates, which form part of the so-called “Ring of Fire”, and experiences up to 15,000 tremors a year.