The declaration, announced on Tuesday, will give the state's director of public health power to order people to quarantine, isolate or evacuate an area.

The powers will initially be used to ban mass gatherings and ensure people arriving from overseas self-isolate for two weeks.

"It is the next step in the proportionate and scalable response we're taking, Premier Peter Gutwein told reporters.

Tasmania has recorded seven coronavirus cases, but none have been transmitted locally.

"This is not a reaction to an imminent threat ... (but) a gradual and steady increase in the proportional way that we're dealing with this," Mr Gutwein said.

The state government will on Tuesday reveal an economic stimulus package and is requiring all people entering the island to fill out an 'arrival card' with their details.

Meanwhile, Hobart's MONA will shut its doors from Wednesday to ensure the safety of staff, visitors, contractors and the wider community.

Owner David Walsh said he had been trying to find a way to keep the museum open but conceded there's a chance MONA could become a "major centre for contagion".

"I'm closing it, without certainty and with some loss of pride, but I'm closing it," he wrote in a statement.

"I hope people care enough to visit when we reopen. I hope that people care enough to understand why we've closed."

Mr Walsh said he grappled with the decision because people need entertainment and a functioning museum might provide relief from the "drudgery" caused by the cancellation of public events.

The museum hasn't recorded a drop in visitors in recent times.

It is not known when MONA will reopen, only that it will be shut for the foreseeable future.

The decision comes after Mr Walsh last week announced midwinter festival Dark Mofo would not go ahead due to financial concerns.

Tasmania on Monday joined NSW and WA in cancelling RSL-held Anzac Day commemorations.

Australian Associated Press