Hipkins said the 32-year-old man, who arrived from India on 3 July, left his managed isolation last night to go to the Countdown supermarket on Victoria Street in central Auckland.
The man was outside the facility for 70 minutes.
Hipkins said after CCTV footage was viewed and the man was interviewed, the current assessment of the risk to the public was low.
"The person wore a mask although indicated that was removed for short periods of time."
In a statement, Countdown said the supermarket closed for cleaning at 8.15 this morning and will reopen tomorrow.