The category two storm, packing gusts up to 140 kilometres an hour, made landfall on the main island of Viti Levu this morning and had been moving south-southwest towards Suva since.
The Fiji Meteorological Service's, Sakeasi Waibuta, said many parts of the country had already suffered from severe flooding with over 100 millimetres of rain overnight and the downpours continuing today.
"Many parts of Fiji is flooded, especially in Vanua Levu. The associated rainbands that [Cyclone] Ana brought on the eastern flank of the cyclone over Vanua Levu, Lomaiviti and the eastern parts of Viti Levu, they have been experiencing heavy rain and very strong winds."
RNZ Pacific reprots the townships of Labasa, Ba, Korovou and Nadi had already reported major flooding with some roads completely underwater.
The government also reported that the Rewa River had burst its banks, with water pouring into the Syria Park area of Nausori.
Waibuta said while it was too early to know the full scale of damage from the storm, the winds could be destructive.
"We've already sent out a warning that there will be severe damages to weak structures and trees and especially vegetation and crops, there will be huge damages to them as well."
Cyclone Ana was expected to move to the south of Viti Levu this afternoon.
However Waibuta warned although forecast to move away from Suva it would still continue to bring destructive winds and heavy rain to the area into the night.
"The weather surrounding all those areas it is all covered in the strong winds, the radius. So we will be expecting these until tonight and as it heads south further the winds will ease but the associated rain bands will continue to affect us"
Cyclone Ana is forecast to sweep over the island of Kadavu overnight.
Meanwhile this afternoon, Education Minister Rosy Akbar, announced that all schools in Fiji would remain closed until further notice.
This storm is the second cyclone to hit Fiji in just over a month after Cyclone Yasa killed four people and severely damaged villages in December.
Photo Fiji Red Cross