The Fiji National Disaster Management Office said one person was in intensive care and more than 2,500 people had moved to 70 evacuation centres.
The category two tropical cyclone is not expected to make landfall in Fiji, though its weather service has issued storm and flood warnings for parts of the country.
"Close to its centre the cyclone is expected to have average winds of up to 110km/hr with momentary gusts to 150km/hr," the Fiji Meteorological Service said in a statement.
Cyclone Sarai is moving east at nearly 10 kmh (6 mph) and is expected to move into Tongan waters on December 31.
Tonga's Meteorological Service has issued a heavy rain and flash flood warning for the entire country.
