He understood the individual was cooperating with health officials to identify any locations of interest and close contacts, while isolating at home.
Boult encouraged everyone to keep a watchful eye on the Ministry of Health website for any notified locations of interest in the district.
Anyone who caught a Queenstown to Auckland flight on Sunday morning is considered a close contact, and is urged to self-isolate, test immediately and on day five after exposure.
Flight NZ614 left Queenstown at 9.19am and arrived at 11.03am in Auckland.
Queenstown Airport in Frankton was listed as a location of interest between 8.45am and 9.15am on Sunday morning, while Skyline Gondola Queenstown is a location of interest between 3.30pm and 5.45pm on Saturday afternoon.
Anyone in either locations at the specified times is asked to self monitor for symptoms for 10 days after exposure.
If they develop symptoms, they are asked to get a test and stay at home until they receive a negative test result.
Boult said it was important that people remained calm, supported each other and were kind.
"Whilst we've all done great work in getting vaccination and booster numbers up and following Covid Protection Framework red setting practice, it's time to double down and keep ourselves and each other safe and healthy," he said.
"This may feel confronting with our district having been free from Covid for so long, but we knew it was coming. Over the coming weeks and months, we are highly likely to see more cases pop up, so have a chat to your household about what you would do in case you had to isolate at home. Do you have enough groceries, pet food and medication, or do you have someone who can drop supplies at your door?"
Boult said he was happy with the self-isolation capacity in place for his district.
Locals and visitors alike are reminded to follow the public health measures.
Investigations into the origins of the case are ongoing.
The Southern District Health Board said testing is available throughout the southern district.
People are urged to get tested if they have cold or flu like symptoms, even if they are mild or if they have been at a location of interest.
Testing is available at the Queenstown Medical Centre with bookings, and a drive through and walk-in testing are available at the Engage Safety Covid-19 Testing Centre and Te Kāika Testing Centre in Frankton.
- RNZ
