People who were at Animates Manukau on Saturday, 21 November between 1.22pm and 2.11pm were advised to get tested.
Notifications were being sent through the Covid Tracer app to people who scanned in around this time.
"People should note that the risk is deemed to be low and testing is being recommended as a precaution only," the ministry said.
The Air NZ staffer also made brief visits to a number of other businesses and shops on November 20 and 21.
Staff at most of these businesses were being advised to isolate at home and get tested if they developed symptoms. Members of the public who were at these locations were not considered to be at risk.
Further locations may be notified as the investigation continues.
Other staff on the Shanghai flight were initially being assessed by Air New Zealand around their contact status.
Auckland Regional Public Health would be following up with any close contacts when the staff members were back in New Zealand.
The number of confirmed Covid-19 cases in New Zealand is now 1675. There are 53 active cases.
The staffer tested positive for Covid-19 in Shanghai on Sunday after arriving on a direct flight from Auckland. They tested negative on Wednesday during routine border testing in New Zealand, and they had not worked on any other flights before the Shanghai trip.
Preliminary investigations showed that the person's movements in New Zealand for the past two weeks appeared to have been confined to Auckland, Hipkins said.
Their circle of close contacts also appeared to be "relatively small", though he was due to receive a further update this morning. Contact tracers were re-tracing the person's last two weeks in Auckland.
The person's flight schedule in the past month included flights to Australia and China, Hipkins said.
"Coming back from a higher risk place like China - they should be doing a 48-hour stand down and a negative test at the end of the 48 hours before they can go back out into the community.
"We're checking to make sure all those things have happened."
The cabin crew member had mild symptoms and was being re-tested. The rest of the Air NZ crew did not have symptoms and had tested negative.
They are returning to New Zealand tomorrow and will go into isolation. There would be genomic testing of the positive case to track where they might have caught the virus from.
Hipkins said genomic sequencing, which has proven to be a vital tool in the Covid-19 response during recent outbreaks, would be done as soon as the crew member landed in New Zealand.
Hipkins also said work was under way to decide how much of the New Zealand population would need to be vaccinated before travel restrictions could be dropped.
"One of things we're looking at is percentage of the population before we can remove all travel restrictions. It doesn't necessarily have to be 100 per cent. We may never get to 100 per cent."
New Zealand's borders have been closed to non-residents since March, with some exemptions for essential workers.
