The storm had earlier been upgraded from a category one to a category three system, with winds gusting up to 170kmh at its centre.
But the Fiji Meteorological Service said the system started to weaken overnight.
It said the cyclone was moving east-southeast at about 45 kmh towards the southern Lau group of Ono-i-Lau, and should be entering Tonga waters after midday yesterday.
Close to its centre, the cyclone is estimated to have average winds of 110 km/h and momentary gusts to 155 kmh.
A strong wind warning remains in force for the rest of the Fiji group and a hurricane warning is in force for Vatulele, Beqa, Kadavu and nearby smaller islands.
It is just six weeks since Cyclone Winston claimed 44 lives, left tens of thousands homeless and caused widespread destruction.
The government has imposed an indefinite nationwide “Restriction of Movement” order.
Though the current storm is weakening, the country-wide curfew activated by the National Disaster Management Office remains in place until further notice.
The curfew was to preserve safety and public order during the expected storm, and people have been told to remain indoors until advised otherwise.
The Fiji Police Force, in support of the Emergency and Discipline Services, have been out ensuring the curfew is being implemented.
FBC News reported that only movement by emergency and essential services personnel will be permitted.
“To preserve safety and public order prior to the arrival of Tropical Cyclone Zena, all members of the public are to remain indoors and secure their properties until further notice,” an official statement said.
The government also announced schools were to be closed, while all international flights and most domestic flights were cancelled on Wednesday.
Neville Koop from the Nadraki Weather Service said the cyclone was taking a different path to that of Winston.
“This is going to affect the Coral Coast, Pacific Harbour, Suva and islands to the south of us,” he said.
“Fortunately the people in the north will be spared the worst of the winds, but the rainfall and the flooding is really the devastating impacts we’re experiencing right now across the country.”
Another 200 millimetres of rainfall was expected across the country within 24 hours.
Pacific Harbour resident Sakiusa Bolaira said people were expecting the worst.
“Nobody’s taking any chances now. Everybody is stocking up and preparing for the worst,” he said earlier on Wednesday.
“We’ve seen what tropical Winston has done to our fellow Fijians on the other side of the island, but I guess on this side of the island it is our turn.”
Heavy rain from a previous severe weather system caused flash flooding on Viti Levu earlier this week.
Police reported a 70-year-old man a 13-year-old girl had drowned while crossing a swollen river in separate incidents.
With widespread damage to homes across the country, many have returned to shelters used when Cyclone Winston hit in February.
Some 80 evacuation centres have been opened with over 6400 people taking shelter.
CARE International’s Siobhan Talty said despite the new cyclone tracking a different path, people affected by Cyclone Winston were still struggling.
“Over the past few weeks we’ve seen a trend of people going back to their homes to rebuild, replant their gardens and that kind of thing but now they are having to pack up and go back to the evacuation centre, which is crowded,” she told the ABC.
“The facilities aren’t great and in terms of morale it’s not a very nice situation to be in and it’s really taking everyone a step back.”
Meanwhile, the Red Cross said volunteers were ready to distribute water purification tablets, jerry cans, and tarpaulins but had to wait for the weather to clear. - PNC