Thousands on the country’s east coast have fled after a warning to move to higher ground.
The Civil Defence Ministry said people close to the epicentre could see waves three to five metres high.
It described the tsunami as “an event of life-threatening or national significance”.
Waves of up to between 1.5 and two metres have already hit the Kaikoura area and smaller ones hit Castlepoint and Wellington, said New Zealand’s Geonet group.
The Civil Defence Ministry tweeted: “A tsunami has been generated, the first wave has arrived in the North Eastern Coast of the South Island.”
It added: “The first wave may not be the largest. Waves may continue for several hours.
“If you are in a low lying area on the East Coast of the North, South or Chatham Islands move immediately to higher ground.”
St John Ambulance said it was sending helicopters carrying rescuers and doctors to the epicentre of the quake – 57 miles (91km) north of the South Island city of Christchurch.
There were no immediate reports of any deaths but some reports of injuries were coming through, said St John’s.
The quake hit just after midnight local time, according to the United States Geological Survey (USGS).
The initial tremor was followed by aftershocks, including several above magnitude 6.
Sony PlayStation 4 Pro – 1TB
Sirens sounded in Christchurch – badly damaged by in a deadly 6.3-magnitude quake in 2011 – and strong jolts were reported in the capital, Wellington, some 120 miles (200km) north.
There was gridlock on roads leading to Mount Victoria – a hill overlooking the capital.
Prime Minister John Key tweeted: “I hope everyone is safe after the earthquake tonight.”
New Zealand’s Geonet, which describes itself as the official source of geological hazard information, listed dozens of quakes between 3.8 and 6.6.
Hugh Sintes, from Christchurch, told Sky News: “My wife had gone off to the bathroom, I had just lay down on my bed and all of all of a sudden the bed started wobbling and it got more and more intense.
“And I thought ‘okay this is getting a bit serious’. It continued on and on – it got quite concerning.”
The relatively shallow first quake occurred at a depth of six miles (10km). Shallow tremors are felt more strongly on the surface.