The 40-year-old made the shopping trip in Launceston after he left the hospital on Sunday night.
He was told to go straight home and quarantine himself until his results came back.
He spent around 15 minutes at the Launceston store, on the corner of Wellington and York Streets, at 10pm.
He was confirmed to have the virus the following day on Monday.
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.