Falling trees cut power and blocked roads on the main island of Viti Levu, where all flights were cancelled as high winds buffeted Nadi international airport.
Many residents spent the night huddled in evacuation centres where they were given food and water.
Suva resident Danny Southcombe said the capital escaped the brunt of the storm but was still brought to a standstill.
"It's not too bad here in Suva. We weren't that badly damaged, just a few panels flew off the house," he told AFP.
"It's pretty calm now but when I look around all I can see is trees on the road."
The acting head of the Red Cross' Pacific office Ahmad Sami said a proper damage assessment would take time.
"But we anticipate that humanitarian needs will be very high," he told AFP.
"This is the first time that Fiji has experienced a cyclone of this magnitude in their history, a category five, so we're still trying to find out the figures."
He said priorities were restoring power and repairing damaged homes, as well as maintaining drinking water supplies in more than 700 evacuation centres.
The Fiji Meteorological Office said it had moved out to sea about 230 kilometres west of Nadi by mid-morning Sunday, although the islands could still expect strong winds, heavy rains and powerful swells.