Visits to Tasmanian prisons will be temporarily suspended from this weekend and the state's budget will be delayed until at least October, Premier Peter Gutwein confirmed on Saturday.
Mr Gutwein's announcement came after a woman in Southern Tasmania was diagnosed with coronavirus on Friday.
Coronavirus: All the latest updates on COVID-19 for Tasmania
The woman arrived back in the state on Wednesday after travelling to the United Kingdom and developed symptoms a day later.
She was assessed and deemed well enough to be managed at her home, Tasmania's Director of Public Health Dr Mark Veitch advised.
Dr Veitch said authorities would follow up with the airline and passengers who were seated two rows behind, and in front of the woman.
"We don't believe there are any community contacts relevant there," Dr Veitch said at a media conference with the Premier and Health Minister Sarah Courtney.
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Mr Gutwein urged Tasmanians to comply with strict new rules designed to protect the public and minimise the spread of coronavirus.
"If you don't need to go out, don't," Mr Gutwein said.
"Be cautious, be responsible and importantly abide by the rules because the penalties will apply and they will be substantial."
Pubs, restaurants, bars and other venues must not allow more than 100 people inside with a limit of one person for every four square metres now in force across Australia.
"What that means is up to 100 people can be in an area up to 400 square metres, 50 people in an area of 200 square metres, 10 people in an are of 40 square metres," Mr Gutwein said.
"It's important that venues and patrons adopt these rules. Don't put your health and safety, or the health and safety, of other people at risk."
From this weekend, Mr Gutwein confirmed personal visits to prisons in Tasmania would be temporarily suspended.
"The Tasmanian Prison Service will increase telephone access for prisoners where possible and will put in extra resources into alternative communication measures such as video calls to ensure prisoners can remain in contact with their families and friends," he said.
Legal practitioners will still be able to visit prisoners but they must follow self-assessment and hygiene guidelines in line with public health advice.
Mr Gutwein also said the state budget will not be handed down until at least October and suggested the government would implement further financial stimulus measures to deal with the economic fallout of the coronavirus.
"In terms of revenue, there is no clarity in terms of the revenue situation," he said.
"It's important that we ensure that when we bring down a budget, that we bring down a budget that is meaningful."