The new cases were among the 1043 infections confirmed by the ministry on Sunday.
Over 14-thousand positive people are in isolation in the western and central divisions.
Health Secretary James Fong said the five patients are being isolated at the Levuka Hospital.
He said three of them were recorded on Ovalau while the other two on Gau.
He said the ministry is working with the Lomaiviti Provincial Council to monitor the situation on both islands.
Dr Fong said the COVID cases on Ovalau were contractors for the Roads Authority, who had recently arrived on the island.
He said the virus was first detected on Gau after crew members of a vessel carrying cargo arrived at the island, a few weeks ago.
Dr Fong is urging residents in the maritime islands to be cautious when vessels carrying cargo arrive there.
"People must wait for their luggage to be offloaded and for the health officials to complete the decontamination process before they collect their freight."
Dr Fong said inter-island operators must also ensure all safety processes are followed when operating in the outer islands.
Fiji now has 14,247 active cases in isolation with 113 deaths reported, 111 of them from this latest outbreak that began in April.
Photo file Caption: Levuka Hospital in Fiji's Eastern Division