In a statement, the ministry said public health officials in Waikato were continuing to investigate the case of the traveller to Hawke's Bay.
One location of interest, Kmart Napier, has been identified and anyone there between 3.53pm and 5.13pm on Friday, October 15, is asked to monitor for symptoms for 14 days.
If any develop, people are being told to get tested and stay at home until a negative test result is received and they have been symptom-free for 24 hours.
No further locations of interest in Hawke's Bay have been identified as at Friday.
However, locals are asked to keep checking the Ministry of Health's website, where locations of interest are updated.
There have also been no positive detections for Covid-19 in the most recent wastewater samples collected from Hastings (October 19 and 20), Napier (October 18 and 20), and Wairoa (October 15 and 19).
Further samples from these sites will be collected next week, the ministry said.
Napier mayor Kirsten Wise and Kmart Napier assured locals the traveller was a "low risk" for the city because they obeyed Covid level guidelines.
"The information that we've had from the DHB is that it is a very-low risk case and the person did follow all the guidelines while they were here," Wise said.
"So just to reassure our community, I think it is low risk, and if anyone was at that location of interest, at Kmart, then ... absolutely get tested if experiencing any symptoms."
Wise said she did not know why the traveller was visiting Hawke's Bay.
She also told Radio NZ that while no one liked to hear there had been a positive person in their community, local authorities had been preparing for the eventuality.
"Ultimately with this Delta strain we all know there's a likelihood this will end up in our community and the DHB has been working really hard to prepare for that."
Testing stations around the region were "all set up and ready to go" over the next few days, and Wise hoped to see increased turnouts at vaccination clinics over the weekend.
"This may go and also prompt some people to get their vaccinations done."
In a letter addressed to staff and their families, Kmart also advised it had been told the case presented a "low risk", adding "no further action was required".
The customer signed into the store and was wearing a mask. They displayed no symptoms during the visit, the letter stated.
Staff were asked to isolate at home if they began to experience any symptoms and to get a Covid-19 test.
Two of the person's close contacts in Hawke's Bay have returned negative day six tests.
One of the close contacts lives in Napier and the other in Wairoa but was visiting Napier on the Friday the traveller was in the city.
Jeremy Harker, chief executive of Quality Roading and Services (QRS), took to social media to praise one of his business' employees who was identified as a close contact of the traveller.
A post on the company's Facebook page said: "At QRS we stand alongside our employee and feel nothing but gratitude for the steps they have taken to keep others safe from infection. It was exactly the right thing to do."
The close contact was double-vaccinated and had been proactive in seeking information and following advice from health officials. They were isolating at home.
"I understand this may cause some anxiety in Wairoa so at this time I cannot stress enough that we need to look out for each other," the post read.
"Those who are tested for the virus should be supported for taking action to check."
The two contacts would also have a day 12 test next Wednesday, a Ministry of Health spokesman said.
It has so far declined to share the vaccination status of the Covid-positive case, citing privacy.
The ministry has also been approached for further comment about why an exemption was approved, and whether exemptions to travel are allowed for those who have not been vaccinated.
If you were at Kmart last Friday between 3.53pm and 5.13pm the advice is:
- Self-monitor for Covid-19 symptoms for 14 days after you were exposed at this location of interest.
- If symptoms develop, get a test and stay at home until you get a negative test result and until 24 hours after symptoms resolve.