That is separate from any tsunami risks from the Tonga volcano although MetService said people should be alert for high waves over the coming days.
Its aviation team has been issuing advisories to ensure no planes fly through the cloud of volcanic ash from the eruption yesterday of the underwater volcano Hunga-Tonga-Hunga-Ha'apai.
MetService said Cyclone Cody is currently over waters to the northeast of New Zealand, is expected to move southwards and pass far to the east of East Cape tomorrow, and then track south towards the Chatham Islands on Tuesday.
Head of weather communication Lisa Murray said: "Wave buoys have already recorded large waves for northeastern coasts. These are separate to the tsunami wave from the Hunga-Tonga- Hunga-Ha'apai volcano which has affected parts of New Zealand.
"We are advising people to be on alert for high waves over the coming days.
"Waves of this size and direction mean that they will be seen in places that rarely see large waves and are usually considered safe for swimming, so please take care."
MetService is also the volcanic ash advisory centre for Tonga's volcano so its aviation team has been ensuring no one flies through the cloud of ash thrown up in yesterday's eruption.
"We are also providing forecasts to the Ministry of Foreign Affairs and Trade in support of the relief effort."
- RNZ