The fifth person who tested positive to coronavirus is believed to have caught the illness in North America, Health Minister Sarah Courtney said.
She said none of the five cases are believed to be community spread - meaning the infected people brought it with them from overseas rather than it moving from person to person within the state.
"All five confirmed cases of coronavirus in Tasmania were associated with international travel, and do not indicate that we have had community transmission here in Tasmania," she said.
"I'd like to assure Tasmanians that the risk from casual contact does remain low, however it is important to remain vigilant."
The fifth case is a man in his sixties who is isolated and in a stable condition in the Royal Hobart Hospital.
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He arrived in Tasmania on Tuesday, March 10.
She said he was not likely to be infectious on his flight home.
"He became unwell after arriving in Tasmania," she said.
"Because of the period of time between him arriving in Tasmania and the onset of his symptoms, he was not infectious on his international or domestic flights."
"I'm advised that it was a small number [of people he had close contact with], and we're in the process of reaching out and liaising with those people who have had close contact."
The other four cases remain in a stable condition and in isolation in Tasmanian hospitals.
As of midday Saturday, 283 tests for coronavirus have been done in Tasmania.