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.
TC Ana developed into a category 3 system as it tracked out of Fiji last night.