A spokesperson for the National Disaster Management Office says south-west Viti Levu and the southern islands of Kadavu and Lau were most at risk.
Penioni Kuinikoro said the worst of the category 3 storm was expected to grip the country between 3pm and 6pm today.
At midday today Tropical Cyclone Keni was about 110 kilometres southsouthwest of Nadi and moving southeast at 17 knots.
The storm has winds at its centre gusting up to 185 kilometres an hour with storm force winds extending out 95 kilometres.
On its current forecast track, Keni is expected to move close to Kadavu this afternoon and Ono-I-Lau tonight, then move out of the tropics on Wednesday afternoon.
It is expected to weaken as it moves into what forecasters call a more unfavourable environment.
Mr Kuinikoro said parts of the western division were already water-logged due to last weekend's flooding and further heavy rainfall had the potential to be catastrophic.
He said people in at-risk areas should be in evacuation centres.
"People are taking the initiative to evacuate but we've got the manpower on the ground. Our military, our police, our fire-fighters, our corrections services - both uniformed and non-uniformed personnel are on the ground throughout the country evacuating people from flood-stricken areas."
The government said people also needed to prepare a three-day family disaster kit, strengthen their homes, be ready for power cuts and evacuate if need be.
It's the second cyclone to hit Fiji in just over a week after Cyclone Josie left six people dead over Easter.
Last week's major flooding in the west and north of Fiji also left two dead at the weekend.
Warnings in force
A tropical cyclone warning remains in force for whole of Fiji.
A hurricane warning remains in force for Vatulele, Kadavu and nearby smaller islands.
A storm warning remains in force for southwest viti levu, from sigatoka to Navua, Beqa and Ono-I-Lau.
A gale warning remains in force for the rest of Viti Levu, Yasawa and Mamanuca Group, Moala, Totoya, Matuku and the rest of southern Lau.
A strong wind warning remains in force for the rest of Fiji.
A heavy rain warning remains in force for the whole of Fiji.
A flood warning remains in force for parts of Fiji.