Supermarkets identified as locations of interest are advertising new jobs as many of their staff are now having to self-isolate.
At least three Countdown supermarkets are currently closed.
Countdown Birkenhead is not due to open again until Monday, August 30.
"We're doing the best we can to manage not only the demand from customers but also a rapidly changing situation in terms of locations of interest," Countdown spokeswoman Kiri Hannifin said.
"Obviously this is very unsettling for our teams right across New Zealand. We're continuing to focus on our safety procedures which are designed to keep our team and communities safe ..."
Hannifin said any staff members who were working during the time of the case visits have been asked to isolate at home for 14 days and to be tested three times, as per the guidance they have been given by Auckland Public Health officials.
An exception has been made for people who worked at the Countdown Lynfield just over two weeks ago, on August 4, when a Covid positive case visited.
"Our team is not required to isolate unless they have or have had symptoms in the past two weeks. If they have symptoms then they are required to be tested."
The Ministry of Health recorded that a positive Covid case also visited the Lynfield supermarket on Sunday between 8pm and 8.15pm.
Staff members who worked on that night are at home isolating for 15 days, a spokeswoman confirmed.
As of midday, 12 supermarkets around the Auckland region have been confirmed to be locations of interest in the past few days, after a Covid positive case or cases visited their premises.
Three supermarket outlets - Countdown Birkenhead, Pak'nSave Wairau and Countdown Lynfield - feature twice on the list.
The other supermarkets affected are New World Green Bay, Countdown Botany, New World Mt Roskill, Countdown Takapuna, Countdown Glenfield, Countdown Glenfield Mall, New World Birkenhead, and Countdown Lincoln Rd in Henderson.
Some stores have started to advertise vacancies in order to replace the many staff who, now considered to be close contacts, are in self-isolation for at least the next two weeks.
New World Mt Roskill is among those calling for new staff after a person who later tested positive for Covid-19 visited on Monday night between 7pm and 7.20pm.
"It's been a challenging day, but we're open and here for your grocery needs," management said on its Facebook page yesterday.
"Due to so many of our team having to stand down and self-isolate, there are staff gaps in checkouts as well as online shopping that we're looking to fill ASAP."
Anyone interested is invited to send an email to the team.
Pak'nSave Wairau is also advertising job positions after a Covid positive case or cases visited the supermarket on Saturday between 3.20pm and 3.50pm and Sunday between 11am and 12pm.
"Rest assured all staff who have been identified as close contacts by the [Ministry of Health] are self-isolating."
The store said it had been a challenging 24 hours since being identified as a location of interest and thanked customers and staff alike for the support - both emotionally and physically by helping to clean the store and stock it up ready for customers the next day.
Anyone with checkout operator experience looking for a job is being asked to apply.
In the meantime, because of the smaller crew, Pak'nSave Wairau has had to reduce its opening hours from today until further notice. The store will now be open from 7am to 8pm.
"We thank you for your understanding."
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