A woman in her 80s has passed away in the North-West Regional Hospital due to illness related to the coronavirus, Premier Peter Gutwein said on Monday morning.
He said the state's first death from the virus was confirmation people needed to understand their quarantine and social-distancing requirements.
Mr Gutwein said countries who did not take appropriate steps early on went into a full economic and social lockdown.
Coronavirus: All the latest updates on COVID-19 for Tasmania
He said he did not want that to occur in Tasmania so further steps would be taken today.
Mr Gutwein said an order would be in place for four weeks for people to remain in their primary residence from midnight tonight.
He said there would be exemptions for people to go to work, gather essential items, exercise or provide personal care, and for students to attend school.
Mr Gutwein said people who were isolating at a secondary property already would be allowed to stay there for the month.
He said police would enforce it and charges could be laid on those who broke the rules.
Mr Gutwein said the Justice Department was looking at the prospect of on-the-spot fines.
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Further details on the requirement for people to isolate in their homes for four weeks will be provided later today.
Mr Gutwein said this order came with another on public and private gatherings would be reduced to two people from midnight.
He said this did not apply to households of more than two people.
Mr Gutwein said playgrounds, skate parks and outdoor gyms would be closed.
"These are tough measures but they are done with Tasmanians' health and wellbeing as a priority," he said.