Visits to Tasmanian hospitals will be banned from noon today under new social distancing measures.
Exceptions will be made for people visiting their partners at the birth of a child, parents visiting dependent children who are sick and for "compassionate and end-of-life reasons".
There have been seven coronavirus cases linked to the North West Regional Hospital in Burnie — six health workers and one patient.
"This outbreak shows how quickly, how easily, these matters can take hold and we need to ensure we get on top of it," Premier Peter Gutwein said.
The Premier also announced visits to aged care facilities around the state would be limited to compassionate and end-of-life visits only.
"What we don't want over the Easter period is people with time on their hands thinking 'what we'll do is pop over and see mum and dad'," Mr Gutwein said.
"We want to ensure we keep the most vulnerable in the state safe."
He said the aged care rules would be reviewed in two weeks.
Tasmania has 89 confirmed cases of coronavirus.
Two people have died and 34 people have recovered.
Easter travel warning
Mr Gutwein used his daily press conference to once again warn people not to travel over the Easter holidays.
"You can't go camping, our parks are shut," he said.
"You can't stay in your shack because you've got to stay in your primary residence.
"We want people to stay home, we need that message to get through."
He said Tasmanians could expect police to be out in force over the Easter break and that anyone staying in their shack or holiday home may receive a knock on the door.
"It is important that we do not take this virus to our coastal communities," Mr Gutwein said.
"Many of them are older, more vulnerable communities."
