The ship's January 18 sailing is still scheduled to go ahead but the company told passengers that sailings may be delayed.
A short Sunset Dinner cruise scheduled for Sunday 19th has also been cancelled by the company.
The operator said passengers would be given free amendments for all affected bookings.
"Please be assured that our captains will be conservative and our passengers and crew are our highest concern," said Jackie Haworth-Charlton, the company's managing director.
On Thursday Haworth-Charlton updated his statement, saying: "It is now forcast to track over Kioa and the Lau group as a category 1 or 2 system so not as severe as first predictions showed. Our thoughts are with the people of Fiji and her islands."
Blue Lagoon told Cruise Critic that it had not cancelled any departures but was waiting further news on the developing weather pattern from relevant authorities. The operator said it would update customers by Wednesday.
Local day cruise operators Awesome Adventures and South Sea Cruises have advised guests who have made bookings to expect disruption.
This is the second cyclone system to pass through Fiji this year, following Cyclone Sarai. Last fortnight, 2000 people were forced into storm shelters as the Category 2 storm battered the island.
Local cruise and tourism operators are cautious of cyclone season following 2016's Tropical Cyclone Winston – a category 5 storm that took 44 lives during, which is the worst incident on record.