Cyclone Percy could directly hit the northern island of Pukapuka in the Cook Islands within the next one to two hours, and it is also expected to pass very close to nearby Nassau.
The 700 people on Pukapuka have already moved to higher ground and are sheltering at the island's school but there's been no contact with the 200 residents on Nassau.
Chief Inspector Teroi John Tini of the Emergency Operations centre says three houses on Pukapuka are already known to have been destroyed as Percy, with winds of 185 kilometres and gusts of over 265 kilometres an hour, approaches the island.
The lead forecaster at the New Zealand Met Service, Paul Bruce, says the cyclone's centre could pass over Pukapuka.
"It's so close at the present time that it may pass directly overhead, and if it did do that, of course, you have a period of calm winds and then the winds pick up again. It certainly will be very, very close so we are forecasting hurricane force winds, up to 100 knots. They'll obviously get phenomenally high seas, and very heavy rain with thunderstorms."
Mr Bruce says Nassau will also be experiencing phenomenal seas and hurricane force winds.
Percy is expected to gradually move towards the south.