The 40-year-old man, who remains in the Launceston General Hospital, was in the supermarket from 10pm to 10.15pm, used the self-checkout and did not wear a mask.

Director of public health Mark Veitch said there was no need for alarm.

"The risk to anyone who was in the supermarket at that time is very low. However, it is appropriate to fully inform staff and customers who were there," he said.

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"We do not anticipate any infections arising from this, but anyone who was at this supermarket around that time on Sunday night and becomes unwell in the next two weeks should contact the Public Health Hotline on 1800 671 738.

"People who subsequently shopped at Woolworths are at no risk, and people can continue to confidently shop at this supermarket."

Supermarket management has been contacted in order to pass information on to staff who were present at the time.

The man visited the supermarket after he was given information about self-quarantine, and Dr Veitch said he was confident that "all public health processes were followed appropriately"

But Dr Veitch said it was "disappointing" that man did not follow the self-quarantine requirements.

"Coronavirus is principally spread by droplets during prolonged face-to-face personal contact, but not from casual encounters such as walking past someone with the infection," he said.

The man had flown from Iran to Melbourne and then on to Launceston on board flight VA-1368 on Saturday.

Dr Veitch said there was no need for Tasmanians to buy up grocery items for fear the virus would spread.

"People in Tasmania do not need to stockpile masks or groceries or even toilet paper," he said.

"It's very important people in Tasmania stay in touch with information we and the Commonwealth provide.

"People should go about their normal business confidently and ensure they're safe."