The Narrow Neck facility is part of the Devonport Naval Base and houses the officer training school.
Last August, the facility was put into lockdown following a positive wastewater sample during the Delta outbreak.
"All personnel are adhering to MOH guidelines around mask-wearing, distancing, hand washing and limiting contact time," the defence force said in a statement.
Given the current number of cases across the country, the spokesperson said it is not unexpected to have cases occur in Navy personnel, especially those in Auckland.
"NZDF has a workplace mitigation framework in place to limit the impact these cases could have on NZDF personnel, tasks and operations."
Last October a crew member on the Royal New Zealand Navy frigate HMNZS Te Kaha tested positive for Covid-19.
The positive test result was returned during routine testing of the ship's crew after a port visit to Guam, the Defence Force said at the time.
On Tuesday New Zealand recorded 19,566 new cases, with 373 people in hospital, including nine in ICU.