Tropical Cyclone Bina formed to the northwest of the country and its centre is forecast to go between Viti Levu and Vanua Levu.
It is expected to remain a category 1 system.
TC Bina was named less than a day after category 2 system TC Ana unleashed her fury on Fiji.
One person drowned and five people are reported missing.
Among the missing are four fishermen and a three-year-old toddler who went with his grandfather to tie up their boat.
More than 7000 people are sheltering in evacuation centres after heavy rain and high seas caused flooding.