The state government on Tuesday will introduce a Tasmanian arrival card for international travellers and Tasmanians arriving home from overseas.
This comes after a seventh case of coronavirus has been confirmed in the state.
A woman in her 50s had been in close contact with a previous confirmed positive case of coronavirus in Tasmania who had recently travelled overseas.
She was aboard a privately-charted yacht for more than 24 hours with the person.
Public Health has not disclosed the location of the woman.
Premier Peter Gutwein said the arrival card would be introduced on Tuesday to allow authorities to keep in touch with people in regards to the coronavirus pandemic.
He said people arriving in Tasmania who had visited an overseas country 14 days beforehand would be mandatorily required to self-isolated for 14 days.
"There will be penalties that would be applied should people not heed that advice," Mr Gutwein said.
Failure to complete an arrival card at airports and the TT-Line terminal from Tuesday could result in a fine of up to $8400.
Public Health director Mark Veitch said fever-checking at airports had been considered.
"What happens if you do screening at the airport is because people aren't necessarily sick when they come through the gate, you miss them," he said.
"It's a very inefficient use of resources."
Mr Gutwein said he encouraged all Tasmanians not to shake hands, kiss or hug anyone other than those in their close family.
He said events with 500 people in an enclosed venue or a large sporting event should not proceed.
"In terms of fairs, festivals and markets where there is a disparate amount of time that people might spend there, and they are moving though an event, those types of events can proceed," Mr Gutwein said.
He said he had received advice that schools should remain open for now.
Of the seven confirmed cases of coronavirus in Tasmania, one has been discharged from hospital.
Dr Veitch said 90 people had been required to self-isolate.
Labor leader Rebecca White said the government needed to introduce more measures to contain the risk of coronavirus spread.
She recommended services be expanded to regional centres to test for coronavirus and implementation of testing at state borders, airports and sea ports.
Ms White said vacant hotel rooms should be procured as accommodation for health workers so they did not expose family member to the virus and for homeless people to self-isolated.