The Ministry of Civil Defence said people living in some eastern areas should stay away from beaches and the shoreline. Those areas include the East Cape, the Chatham Islands, the Coromandel and Banks Peninsula.
The ministry said if a tsunami did hit it would likely be soon after midnight tomorrow local time.
The earthquake shook Chile's capital Santiago. Officials reported one death in a town north of the capital as well as heavy waves in a handful of coastal cities. It prompted authorities to issue a tsunami warning for the entire Chile coast.