A man who tested positive for coronavirus after arriving in Tasmania from Iran left the hospital to enter self-isolation at home until the results came in, but visited a city supermarket to stock up on the way, authorities say.

Key points: The man did not follow the instructions given to him to self-isolate before his coronavirus test results came in, authorities said

The man did not follow the instructions given to him to self-isolate before his coronavirus test results came in, authorities said People who were at the Launceston city Woolworths on Sunday night are being asked to report if they feel ill

People who were at the Launceston city Woolworths on Sunday night are being asked to report if they feel ill The effort to contact fellow passengers who were on the same plane as the man are still incomplete

Announcing the case at a press conference on Monday afternoon, Tasmania's Public Health director Mark Veitch said the 40-year-old man had "limited travel" in Launceston since arriving on Saturday from Iran, via Malaysia and Melbourne.

Today, at a press conference, Dr Veitch said "further information had come to light" that the man — whose name has not been released — chose to visit the Woolworths store in Wellington Street, Launceston, on Sunday night, before his diagnosis was confirmed.

The man "spent about 15 minutes" in the supermarket between the hours of 10:00pm and 10:15pm, Dr Veitch said, adding he was not wearing a mask at the time.

"Coronavirus is principally spread by droplets during prolonged face-to-face contact and we normally define that as more than 15 minutes," he said.

"It is very rarely spread by casual contact and not by walking past someone in the street or in a supermarket aisle."

He said the supermarket was safe to visit.

The man was not wearing a mask when he visited the store, authorities say. ( Google Earth )

Dr Veitch said authorities did not anticipate any infections as a result of the incident, but asked that anyone who was at the supermarket at the time who became unwell over the next couple of weeks to call the public health hotline on 1800 671 738.

He described the actions of the man, who he said was informed of the requirement for self-isolation, as "disappointing".

Dr Veitch said authorities had so far managed to contact 13 of the 15 people who, according to airline records, were sitting near the man on the Virgin flight VA-1368 into Launceston on Saturday.

Efforts to find the remaining two who were close to him and others on the plane had been hampered by incorrect "phone numbers", Dr Veitch said.

"I have spoken to the man's physician … the man is doing well," Dr Veitch said.

On Monday, Health Minister Sarah Courtney said Tasmanians "are at low risk" after the man's positive test result.

"We will continue to keep the public fully informed," she said at the time.

Anyone in Tasmania with concerns or further questions can call the helpline on 1800 671 738 or visit the coronavirus information website.