The number of people who have tested positive for coronavirus in Tasmania has reached 16, the director of public health Mark Veitch has confirmed, with another Tasmanian currently being treated in New South Wales.

Key points: Five cases were diagnosed in Tasmania on Saturday

Five cases were diagnosed in Tasmania on Saturday Public Health says contact tracing of recent cases is still underway

Public Health says contact tracing of recent cases is still underway The Port Arthur historic site announced it would close "for the foreseeable future"

Two people were diagnosed with COVID-19 on Friday and another five on Saturday.

The five cases confirmed on Saturday comprise one woman and two men who were on the Ruby Princess cruise ship that docked in Sydney on Thursday, and a woman and a man who recently travelled together in Europe.

Among the people diagnosed on Friday is a woman who travelled to the state from the United Kingdom on Wednesday.

A Tasmanian woman travelling on the Ruby Princess was also diagnosed on Friday in Sydney after disembarking the ship. She remains in Sydney and is being managed by NSW Health.

Dr Veitch said contact tracing of the recent cases was underway.

"Persons who are identified as close contacts will be required to remain in quarantine for 14 days after contact with the case. This will include persons who were seated near cases on flights when cases may have been infectious," he said,

"Because of the emerging evidence of coronavirus infections among Ruby Princess passengers, both NSW Health and the Tasmanian Department of Health have contacted the 54 Tasmanian residents who were on the cruise."

All passengers have to remain in quarantine for 14 days after returning to Tasmania.

Port Arthur site closes indefinitely

Meanwhile, the Port Arthur historic site management announced the popular convict-era tourist attraction was closing from Saturday for the foreseeable future, causing uncertainty for the rural municipality.

In a statement, the Port Arthur Historic Site Management Authority (PAHSMA) said it had "not come to this decision lightly".

The Port Arthur historic site is the latest to announce it is closing due to the coronavirus pandemic. ( Facebook: Port Arthur Historic Site/Dee Kramer/Above Down Under )

"We have a duty to our visitors, our team and our industry to ensure the health and safety of everyone," the PAHSMA said.

"We sincerely apologise to our current travellers and trade partners and will refund in full any pre-booked tickets.

"We will continue to keep everyone informed and look forward to reopening as soon as possible."

Tasman Mayor Kelly Spaulding said he understood the decision, but said it would take a heavy toll on the local community.

"Employers are obligated to create a safe workplace … it is a shame, tourism has been booming for the last couple of years."

The Cascades Female Factory historic site in Hobart will also close in response to the coronavirus pandemic.

The tourism industry is reeling after the Government's announcement on Thursday that all "non-essential" arrivals would have to self-quarantine for two weeks in a bid to dampen the spread of COVID-19.

The move was widely supported, but was tipped to send the state into recession.