"An investigation to determine the source of the worker's infection is under way," the spokesman said.
"At this stage, public health officials investigating the case have not identified any clear evidence of in-facility transmission.
"The worker is fully vaccinated, has been regularly tested and is now isolating in a quarantine facility."
Due to the current Delta outbreak, the facility near Auckland Airport was being repurposed for people needing to isolate who couldn't do so at home.
"We have got an additional facility that's being stood up at the moment that will bring several hundred additional rooms - that's the Holiday Inn out by the [Auckland] airport," Covid-19 Response Minister Chris Hipkins said earlier this week.
"It's been converted for use for quarantine purposes. That will bring several hundred more rooms in.
"We will need that extra facility coming on in the next 24 to 36 hours in order to make sure we can accommodate extra cases tomorrow and the day after and so on."
Joint head of managed isolation and quarantine Brigadier Rose King said installing air filtration units in returnee and now quarantine rooms at places like the Holiday Inn were not part of the original plan with MIQ facilities.
This news comes after the Crowne Plaza hotel at the centre of the latest community outbreak recently reopened as a managed isolation facility.
An Auckland Regional Public Health Service investigation was under way into a link between a returnee who tested positive for Covid-19 and a public walkway near the facility that was potentially the source of the current Auckland outbreak.