A third person has tested positive for coronavirus in Tasmania, health authorities say.

Key points: The patient has been taken to the Royal Hobart Hospital

The patient has been taken to the Royal Hobart Hospital Hobart has two confirmed coronavirus cases and Launceston has one

Hobart has two confirmed coronavirus cases and Launceston has one The latest positive test comes after Winter festival Dark Mofo was cancelled amid coronavirus fears

The state's Public Health Services (PHS) said in a statement the patient had been taken to the Royal Hobart Hospital.

It brings the total number of cases in Tasmania to three — two in Hobart and one in Launceston, in the state's north.

On Saturday, PHS said a man who had travelled to Hobart from Nepal was diagnosed with coronavirus.

The 20-year-old man did not self-isolate as requested while waiting for test results, and continued working at Hobart's Grand Chancellor Hotel, attended the Australian Ideal College and visited restaurant Cargo at Salamanca and the O Bar nightclub.

A 40-year-old Launceston man, who had arrived from Iran, was the first confirmed coronavirus case in the state.

He too did not immediately self-isolate, visiting a city Woolworths store.

Latest case follows Dark Mofo cancellation

Impacts of coronavirus have been felt around Autralia's smallest state, with organisers announcing on Wednesday that high-profile winter festival Dark Mofo would not go ahead this year.

Organisers said if they had been forced to cancel the June festival at the last minute, the financial impact would have run into the millions and likely ended the event permanently.

"I know that [cancellation] will murder an already massacred tourism environment, but I feel like I have no choice," Museum of Old and New Art (MONA) owner David Walsh said in a statement online.

"Right now, the Government and MONA are each on the hook for $2 million to run Dark Mofo. That's bad.

"What's worse, as far as I'm concerned, is that if we ran Dark and nobody came, I'd lose $5 million or more, because I would have to cover the absent ticket revenue."