There has been more than 95,000 cases of the virus reported in the world - more than 51,000 have recovered. Just over 3200 people have died.
The travelling family member believed to have passed the virus to the Auckland man was a "probable" case but was no longer showing any symptoms, Bloomfield said.
It was "very likely" this person did, in fact, have coronavirus before recovering, but the ministry will not be retesting them.
In addition to proactive tracing of close contacts on this flight by public health staff, contact will be made with everyone on the flight to provide relevant information. A reminder: close contacts are people who were in the same row of seats, the two rows in front and the two rows behind.
Healthline knows the seat numbers and will be able to advise anyone on the flight, whether they are considered a close or casual contact.
Anyone who was on this flight and is concerned or would like information should contact the Healthline number 0800 358 5453. Interpreters are available.
Other people who have been in contact with the man have been asked to self-isolate.
Seven people are under investigation for the virus.
The ministry can do 550 tests a day, but that will be upped to almost 1000 within the coming weeks.
Bloomfield said the ministry would not be disclosing which medical centre the man went to.
Meanwhile, six people who were in quarantine in Whangaparāoa after being on the Diamond Princess cruise ship have been released to go home. None of them had coronavirus.
She said it was important that schools know what's going on.
Prime Minister Jacinda Ardern this morning deferred any detailed comment on the matter to Bloomfield.
From now on, Bloomfield and his officials will have a 1pm briefing every day to provide details of the coronavirus (Covid-19) outbreak and what his ministry is doing in terms of containment.
The latest figures from the World Health Organisation show there are now almost 95,000 cases of Covid-19 in 81 countries around the world.
More than 3100 people have died; more than 51,000 have recovered.
Speaking to media this morning, Ardern called for calm.