Both cases of Covid-19 arrived at Middlemore's Emergency Department on Wednesday night seeking treatment for issues unrelated to coronavirus.
The first was a patient who answered no to all screening questions, however hospital staff noticed a "very minor cough".
The person was then isolated and tested, which returned positive.
The person is now in Middlemore's Covid-19 isolation ward.
The second case was a patient who answered yes to one of the screening questions, which was also a symptom consistent with the non-Covid-related reason for going to hospital.
This person was then tested and given initial treatment.
After learning of the positive result, the second patient chose to self-discharge.
They are now being managed by the Auckland Regional Public Health Service (ARPHS).
"All staff were wearing the appropriate PPE and as such no staff members are required to stand down," a spokesperson said.
"The risk to public health of these events is deemed to be low," the Ministry said.
More information is expected at the 1pm press conference on Friday.