Passengers and crew on the first major cruise liner to visit Western Australia since the start of the COVID-19 pandemic have tested positive for the virus.

Health authorities and the ship's operators, Carnival Australia, have not revealed how many cases are on board the Coral Princess but say they are being managed according to recently established protocols.

That includes the small number with the virus being isolated for five days.

After spending a day in Broome on Monday, the ship was sailing to Geraldton on Tuesday and was also due to dock at Fremantle, Busselton and Albany.

WA Health said it had been advised that some passengers and crew members had tested positive for COVID-19 but the operators were managing those cases on board.

"WA Health has not been asked for assistance in managing the cases," a spokesperson said in a statement.

Carnival Australia president Marguerite Fitzgerald said as a result of early detection and isolation measures, case numbers on board remained steady.

"These guests are being cared for in their state rooms by our medical and support staff," she said in a statement.

"We are pleased to share that all cases on board have been mildly symptomatic or asymptomatic."

Ms Fitzgerald said the majority of the ship's 2000 passengers were unaffected and were allowed to move about freely on board and disembark at upcoming locations.

"This includes Geraldton where any disembarking guests will be required to undertake a rapid antigen test prior to going ashore," she said.

"This is standard procedure and one that is well understood by our guests to protect themselves, other guests, our crew and the community."

But a man who tweeted he was on board the Coral Princess expressed some concern over the situation.

Identified as sydneyguy, he said passengers were not wearing masks in lifts while people in the pool were coughing.

"So many trapped in cabin with little table outside for food delivery. They go on balcony, no mask coughing with guests next door at risk," he tweeted.

A couple on board the ship told AAP by email they "feel safe" and the crew were doing their best to minimise the spread of COVID.

They said staff supervised hand washing before meals and mask wearing was mandatory in dining areas except when eating.

Masks were also mandatory in lifts and theatres where some seats were marked with a cross to ensure social distancing, while hand sanitiser was readily available, said the couple, who did not wish to be named.

WA Health said all cruise ship operators visiting WA must abide by national protocols and have COVID-19 plans.

"In accordance with the protocols, while in WA waters cruise operators should report COVID-19 cases to WA Health 12 to 24 hours prior to arrival in a WA port," it said.

"Those on board vessels who have COVID should isolate for five days."

The Shire of Broome said many of the Coral Princess passengers came ashore, spending Monday in town or on organised excursions.

It said they were expected to inject about $190,000 into the local economy.

But the arrival of the ship was met with mixed reactions from locals.

In social media posts, some welcomed the return of the cruise liners and the boost to the economy while others expressed concern about the health risks, particularly to vulnerable groups.

Large cruise ships were banned from WA waters in 2020.

Those restrictions were lifted in April this year for ships with up to 350 passengers.

Larger ships were allowed to return from October 1.