Auckland Regional Public Health Service has advised Foodstuffs, the owner of Pak'nSave, the customer had no symptoms at the time they visited on Wednesday.
Staff and shoppers who were at the store at the time were considered to be at low risk, Foodstuffs said in a statement.
ARPHS has asked anyone who was at the store at the time to be vigilant for Covid-19 symptoms.
Anyone experiencing symptoms, including a sore throat, new or worsening cough, fever, or loss of smell, should call Healthline for advice.
"We don't test people every single day, we do have a system of regular testing, there was regular testing at the hotel where he was working at the week before," he said on Newstalk ZB's Heather Du Plessis-Allan Drive
"He was picked up in a regular sweep of testing the following week. We do have to monitor people in between times but we don't test them every day."