"At the time the family member was visiting New Zealand, they became ill with symptoms consistent with Covid-19, and the wider household then also became ill.
"At the time, they did not meet the case definition for testing for people with defined symptoms who had travelled from or transited through China. Italy had not at that point been identified as a country of concern. This meant the New Zealand household was not tested at the time."
The diagnosis was discovered after a man recently developed a sore throat and sought testing. His weak positive result and serology test results and case history indicated an old infection of the virus.
"This would mean that the infected family member from Italy is effectively now the first case we are aware of in New Zealand, as they have reported having symptoms on arrival on 21 February, a week before our first reported case on 28 February," the ministry said.
Five other family members have been identified as historical probable cases of the virus.
"Consequently, the other household cases would represent the first locally acquired cases of Covid-19 in New Zealand, given the onset of symptoms from 29 February for the confirmed case."
The cases all originated in the Waikato region.
The ministry said they now present no risk to the public.
"As part of the investigation, close contacts of this man during his recent mild illness have been tested as a precaution and have returned negative tests.
"We have known that some people can return a positive PCR test long after they have recovered from the illness and are no longer infectious."
Epidemiologist Michael Baker said today's case was the longest he'd heard of to show up in a test after the person had first fallen ill.
"The testing is very sensitive and you can get debris from the original infection, which contains RNA, which is enough to be detected months later," he said.
"This person was February, that's the longest I've heard of ... that's really pushing out that maximum duration."
There were questions around what the virus' maximum duration was, but because it was a new pathogen, "no one really knows".