Eleven of the 29 staff are doctors, 13 are registered nurses, two healthcare assistants, a phlebotomist, cleaner and ward clerk.
Four wards are closed to any new admissions and all patients are being managed under strict infection and prevention control measures, including the full use of PPE, and treated as Covid-19 exposed.
RNZ reports a patient showed up at the Middlemore emergency department on Saturday with abdominal pains. He denied having knowledge of being in contact with the virus or being in a location of interest and didn't have any other symptoms.
The ministry said the patient subsequently developed a fever and was later confirmed with Covid-19.
It said the individual was then moved to a dedicated Covid-19 ward.
Three patients who initially shared a room with the case are now in single isolation rooms. One patient has been sent to a managed isolation facility.
Potentially exposed patients currently on the wards were being checked daily for symptoms and tested on days 3, 5 and 12.
On discharge, they were being managed according to ARPHS guidance.
All patients have received further information on the ward.
ED, the Radiology room where the patient had his scan and room where patient stayed on the ward have been cleaned.
In a statement this evening, the ministry said a "national process" was under way across all DHBs to identify and send staff to Auckland to support the Covid-19 response.
"Middlemore Hospital are actively reviewing staffing daily and, like other DHBs in the region, are experiencing significant shortages of both Registered Nurses and Health Care Assistants."
The ministry was working with metro-Auckland DHBs to match available staff to needs and would continue to deploy staff as required to ensure they had the necessary resources.
"Metro-Auckland DHBs are working closely together to manage the Covid-19 positive cases needing hospital level care. The hospitals have been constantly updating their planning for surge capacity which includes preparations for staffing and resourcing additional beds in dedicated Covid-19 wards."