The 31-year-old man, who arrived in Launceston in Tasmania's north on Monday via Melbourne, has since returned to NSW.

He was tested on Tuesday when in quarantine and returned a positive result on Thursday morning.

The man left hotel quarantine in Launceston on Wednesday to return home to NSW, as is permitted under Tasmania's emergency act.

"This is not a case of community transmission. This is a case that has been picked up in quarantine," Tasmanian Premier Peter Gutwein said.

Mr Gutwein also announced Tasmania would shut to Victoria for at least seven days in response to the mainland state's lockdown.

The state's Public Health Director Mark Veitch said the man, who developed symptoms on Thursday, was "probably becoming infectious" when he arrived in Tasmania.

He went straight into hotel quarantine via taxi and there is a minimal risk of exposure to the community as infection control procedures were in place, Dr Veitch said.

"We have a good idea of the movements of this person and the people to whom may have been exposed to him."

"When this person appeared at Launceston Airport without clearance to come to Tasmania they were managed entirely appropriately."

People on flight VA1364 from Melbourne to Launceston on Monday have been advised to isolate immediately, as have people on flight VA808 from Sydney to Melbourne on the same day.

Authorities say it is likely the man has the Delta strain given the outbreak in Sydney, with testing to confirm either way in coming days.

Tracers have identified about 200 contacts including people on the flights, at the airport, workers at the hotel and the taxi driver.

The case has forced the state government to cancel Sunday's sold out AFL fixture between Hawthorn and Collingwood in Launceston.

"We don't know what we're going to find from testing in coming days. It seems unacceptable to have a gathering of 10,000 people in that broad environment on the weekend," Dr Veitch said.

It is the first case recorded in Tasmania this year, with the state's last case occurring in hotel quarantine in December.

Mr Gutwein said the question of whether the man broke public health orders by coming to Tasmania was a matter for NSW authorities.

At a second press conference, Mr Gutwein said travellers without the correct pass would be turned around as quarantine facilities were filling up.

"We're getting very close to there being no room at the inn" he said.

Tasmania has ordered all hospital and aged care visitors to wear a mask.

Australian Associated Press