The cyclone was downgraded to a category two on Monday afternoon as it moved towards Fiji's southern Lau group, but Misaeli Funaki, a forecaster at the Fiji Meteorological Service, said the storm still had damaging winds as high as 155 kilometres an hour.
Mr Funaki said Winston was expected to pass close to the islands of Ono-i-Lau and Kadavu overnight, bringing with it damaging winds, heavy rains, rough seas and squally thunderstorms.
He said people in the cyclone's path should be prepared.
"It's still a very serious threat to the Lau group on the track that it's currently moving on. The last couple of hours or so it's been moving consistently in a northeasterly direction.
"It could be damaging houses which are not tied in properly and could blow some houses and even trees, and uproot trees and damage plantations," he said.
Mr Funaki said cyclone Winston was expected to re-intensify into a category three as it moved northeast towards northern Tonga -- an unusual direction for cyclones in the South Pacific.
Tonga's Meteorological Office issued its first cyclone warning on Monday evening, warning that Ha'apai, Tongatapu and 'Eua could expect gale force winds as high as 110 kilometres an hour overnight.
There are also warnings for very rough seas in all of Tonga and most of Fiji.