The Associated Press quoted the police as saying the woman had been swept away late on Friday after she saved her two children from a storm surge.
Elenoa Osborne, a journalist with Fiji Broadcasting Corporation, told Al Jazeera that some areas had been flooded and many residents moved to shelters.
"Villages have been moved to higher ground, and some moved to evacuation centres around the country," she said.
"At the moment, a curfew is in place in central, eastern and northern parts of the country, to minimise the movement of the public and ensure their safety.
"Currently there are over 200 evacuation centres, with over 5,000 evacuees and its expected to increase."
| A cyclone in December killed three people and forced thousands to flee home [EPA]
The country's disaster management office had warned thousands of people living on the coast of outer islands in the path of the cyclone to move to higher ground because of expected floods.
Pajiliai Dobui, the director of Fiji's disaster management office, said that the cyclone was likely to be the most powerful storm in recent years.
"Our worry is how devastating the cyclone will be," Dobui told Fiji radio.
Fiji's meteorological service has classified the cyclone as a Category Four storm, the second-most destructive rating on a five-point scale.
The storm was expected to intensify later on Monday and into early Tuesday, with average wind speeds rising to 200km an hour, and gusts of up to 270km an hour, forecasters predicted.
Forecasters have said that the eye of the cyclone is expected to pass to the east of Vanua Levu and the largest island Viti Levu, although many smaller islands would be close to its path.
Schools across the country were closed on Monday and most public services suspended.
In December, Cyclone Mick hit Fiji, killing at least three people, causing flooding, damaging homes and forcing thousands of people to flee to shelters.