Tasmania has three more confirmed cases of coronavirus, bringing the state's total to 10

A woman and two men, all in their 40s, have tested positive to the virus, the Tasmanian Government announced on Wednesday.

The Department of Public Health said it had "commenced an investigation of each of these cases and will be identifying and contacting their close contacts so they can be placed in quarantine".

Dr Mark Veitch, director of Public Health, said all three cases have recently travelled to Tasmania from overseas.

"They are not connected to any previously confirmed cases in Tasmania," he said.

The announcement comes as two Tasmanian nursing homes advise they have been put into lockdown, with families notified they will no longer be able to visit for the next four weeks.

Visitors are also being told to stay away from the Hobart's Roy Fagan Centre specialist hospital to try and stop its vulnerable and elderly patients being exposed to the coronavirus.

Today, further steps in mitigating the effects of the pandemic included the cancellation of Hobart's iconic Salamanca Markets, a major tourist drawcard and one of Tasmania's most visited attractions, which will close for an initial two-week period as the state grapples with coronavirus controls.

The Tasmanian Government has also unveiled its arrival card — a requirement for people to register as visitors to the state, with details of where they have been, where they plan to self-isolate and other details.

Penalties for not completing the card include fines, imprisonment, or both.

All Catholic masses in Hobart have been suspended until further notice due to the coronavirus pandemic.

Parish churches will still be open for visits and personal prayer at times determined by each parish.

Priests will still respond to calls to assist the dying, but any weddings that have been planned will only be open to the bridal party and immediate family.

Mass and the Easter services will be live-streamed from St Mary's Cathedral.

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'Complexities' in following ban on gatherings of 100 or more

In a statement, Minister for Small Business, Hospitality and Events Sarah Courtney said there were a "range of complexities" in introducing the Federal Government's ban on indoor gatherings of over 100 people, announced today.

"Further information will be available to venue operators and the public within the coming days to help guide decision making," Ms Courtney said.

"These are challenging times, and as the situation evolves we will continue to explore ways to better support and protect Tasmanians and their livelihoods."

Ms Courtney said people whose business has been affected by cancellations both now and in forward bookings due to the coronavirus could contact Business Tasmania on 1800 440 026 to discuss their situation.