Much of the main tourist town of Nadi was underwater as Josie, with wind gusts up to 100kph caused widespread flooding before moving away from the island group, AFP reported.
Police director of operations Livai Driu told the Fiji Village website that five people were washed away and "police have retrieved four bodies".
The search was continuing for a missing 19-year-old man.
The National Disaster Management office said more than 1,000 people were sheltering in evacuation centres while heavy rain and strong wind warnings remained in place for Monday.
Photos and videos posted on social media showed cars and buildings engulfed in floodwaters.
"Nadi town and some villages are all drowned," said one message.
"The cyclone has already killed five people. So many people have been left without basic needs," read another.