Fiji disaster management officials lost all contact with Cikobia as the cyclone hit the island with winds at its centre gusting to 250kph.
"Some 65 people evacuated to caves (on Cikobia) and houses were flattened this morning, but we have no reports of any deaths or injuries," Donu said.
Cikobia, a small northern island, has a population of about 100 people.
"There's a lot of destruction of houses, vegetation and garden crops," Viliame Puimanu, disaster management office spokesman, said.
A government patrol boat with emergency supplies was to travel to the island on Saturday afternoon, and an aircraft was being sent to carry out an aerial survey, he said.
People in the Lomaiviti and Lau island groups and on Vanua Levu, Fiji's second main island, escaped serious damage and there have been no reports of injury so far, he noted.
"It's very much a huge relief, especially since there's no major damage to most of the country's northern region," Puimanu said.
As Daman struck the Labasa area of northern Vanua Levu, landslides sparked by heavy rain closed some highways, flooding hit low-lying areas, and strong winds destroyed trees.
Donu said by the time the cyclone reaches the Tongan islands "its wind intensity will be down to storm force - 50 to 60 knots (88-106 kph; 55-66 mph) and gusting up to 105 knots (185 kph; 115 mph).
"At that point it will be a Category 3 storm," she said.
Donu said Tonga "should also expect heavy rain at times and squally thunderstorms".
About 110,000 people live on Tonga's three main island groups of Vavau, Haapai and Tongatapu.