The cyclone is currently about 275 kilometres southwest of Ono-i-Lau with winds of between 110 and 155 kilometres an hour at its centre.
It says damaging gale force winds can be expected, as well as heavy rains, rough seas and squally thunderstorms.
Current forecasts predict that Winston will remain a category two for the next day before possibly re-strengthening to a category three.
Severe weather warnings are in force for Fiji's south as cyclone Winston continues to track towards the islands.
The Fiji Metservice says Winston is moving east-northeast and is expected to move close to Ono-i-Lau and Kadavu tonight.
It says damaging gale force winds can be expected in the southern islands, as well as heavy rains, rough seas and squally thunderstorms.
The cyclone is expected to continue northeast towards Tonga's Ha'apai islands.