Meanwhile, preparations are underway in Tonga with the capital, Nuku'alofa, sitting directly in Tino's path.
The cyclone, which was upgraded to a category one early on Friday morning, was strengthening as it sat the south of Fiji's western Rotuma island, the Fiji Meteorological Service said.
But it was gathering strength as it moved southeast, where it was heading straight for Fiji's second-largest island, Vanua Levu.
Warnings had been issued for much of the country, with torrential rain, strong winds, and damaging swells forecast.