We are prepared to face a very strong cyclone and are urging people all over the country to be prepared as well," he said.
"Our officers are stationed in every part of the country to assist our people and evacuation centres have been set up for people who may be at risk in their respective homes."
Tuifagalele said people were urged to take necessary precautionary measures at the earliest opportunity.
Winston has been moving around the South Pacific for a week, skirting around Vanuatu and Tonga and has previously taken aim at Fiji before veering away.
The UN humanitarian agency UNOCHA said it was ready to support the disaster management office if required.
Winston had the potential to bring "destructive winds, heavy rains, dangerous storm surge and a high risk of both flash and river flooding", UNOCHA said in a statement.