Another was a returnee to New Zealand in managed isolation while the health worker worked in Auckland's quarantine facility.
It is yet unknown whether the health worker was infected from the community or from within the quarantine facility, said the ministry, reports Xinhua.
The ministry said it was the first time a staff member at the Jet Park quarantine facility had tested positive in five and a half months of operation. The facility was used to manage people in quarantine after they test positive for COVID-19.
Currently, three people were in hospital with COVID-19, including two in ICU, the ministry said.
Read Also: Coronavirus: Global death toll 919,081
The number of active cases in New Zealand reached 97, including 39 imported cases in MIQ facilities and 58 community cases.
Meanwhile, the total number of confirmed cases in New Zealand was now 1,446, which was the number the country reported to the World Health Organization (WHO).
Laboratories across New Zealand processed 7,211 tests, bringing the total number of tests completed so far to 864,469.
New Zealand will remain at COVID-19 Alert Level 2 until Wednesday, with extra restrictions in place for its largest city Auckland. A decision will be made by the New Zealand government on Monday on the new Alert Level.
Coronavirus cases were first reported in China in December last year. The World Health Organization declared the crisis a pandemic in March.
The number of globally confirmed cases stood at 28,660,123 on Sunday morning as the death count soared to 919,081, according to Johns Hopkins University.