The warnings come less than two weeks after Auckland was hit by historic levels of rain, which killed four people, caused widespread flooding, landslides and a clean-up bill in the hundreds of millions of dollars.
Auckland Emergency Management said it was working with MetService, the meteorological agency, to track Cyclone Gabrielle.
It said residents should check in with neighbours, family and friends who might need help preparing for the storm.
Gabrielle is sitting in the Coral Sea but is forecast to track south toward Aoetearoa, New Zealand, in the next few days and near the North Island on Monday.
Forecasters expect to it bring heavy rain to the upper North Island, including Auckland, causing severe gales, large waves and storm surges.
New Zealand weather forecaster WeatherWatch.co.nz said the cyclone, which will most likely become a category three this weekend, will reach the country between Sunday and Tuesday.
Category three cyclones have winds of 119-157 kilometres per hour, with gusts up to 224kp/h.
"If this current modelling comes true, this will likely be the most serious storm to impact New Zealand this century - especially with Auckland being in the mix for a potential direct hit," WeatherWatch.co.nz said on Wednesday.
It added that the potential weather event would be concerning even if Auckland had not recently experienced serious flooding.
Roughly one cyclone affects New Zealand each year.
However, MetService said the characteristics and structure of any tropical cyclone will change dramatically by the time it reaches New Zealand and it will almost certainly be re-classified as an ex-tropical cyclone.
"Re-classification as an ex-tropical cyclone does not necessarily mean the system has weakened," MetService said.
