The next day test results confirmed he had the virus.
The Tasmanian Director of Public Health Dr Mark Veitch said the man's decision to go shopping was "disappointing".
"The risk to anyone who was in the supermarket at that time is very low," he told reporters.
"However, it is appropriate to fully inform staff and customers who were there."
Anyone who was there around the same time and becomes unwell in the next two weeks is advised to contact the public health hotline.
"I am confident that all public health processes were followed appropriately, and it is disappointing that the man did not follow the self-quarantine requirements," Dr Veitch said.
He said the 40-year-old man had "limited travel" in Launceston since arriving on Saturday from Iran, via Malaysia and Melbourne.
He said authorities had so far managed to contact 13 of the 15 people who, according to airline records, were sitting near the man on Virgin flight VA-1368 on Saturday.