The missing include a 3-year-old boy, according to RNZ reports.
Tropical cyclones are categorised in strength from 1 to 5, with 5 being the most intense.
Ana is unlikely to directly impact New Zealand but the ex-cyclone later this week may bring rougher eastern coastal conditions.
A second storm, Cyclone Bina, is expected to bring more rain and wind to Fiji's main islands in the next 24 hours but should remain a category 1 system.
WeatherWatch says it is very rare for two tropical cyclones to affect one nation in two days.
The third, Cyclone Lucas, is in the Coral Sea moving eastwards towards Vanuatu and New Caledonia.
The category 2 storm is expected to reach New Caledonia's Loyalty Islands by Wednesday.
Forecasters say New Zealand is not directly affected by the three cyclones because of strong high pressure dominating the country in the first half of February.
But some showers and easterly winds may develop in northern New Zealand along with an increase in eastern swells, waves and rips.
Tropical cyclone season in the southwest Pacific officially starts in November and lasts until the end of April.
On average, at least one ex-tropical cyclone passes within 550km of New Zealand each year, says the MetService and national environmental science institute Niwa.
Significant rainfall, extreme winds, hazardous marine conditions and coastal damage are all possible leading up to and during these events.
