Bloomfield said even though the tested had returned as negative, New Zealanders should remain vigilant.
He thanked the patient for "doing all the right things", including self-isolation after developing symptoms.
Anyone who had been in close contact with a person who had contracted coronavirus, or who had been in Wuhan city within the past fortnight should self isolate themselves, he said.
"We have a result - it's encouraging that the result was negative and of course, fantastic for the person," Bloomfield said.
Auckland City Hospital was well prepared, with Bloomfield saying "our systems were ready".
The patient was treated correctly and treatment for their illness was ongoing, Bloomfield said.
Meanwhile, the Ministry of Health was reviewing its border measures, particularly whether it would have to restrict entry to the country.
It comes after President Donald Trump signed an order temporarily barring foreign nationals from the United States if they had travelled to China within the past fortnight.
If people were symptomatic, Bloomfield reiterated they should immediately seek medical advice.
"People should be empowered to do so and that is how, as a country, we will be able to ensure that ... we don't get a sustained community outbreak"
Border screening was only a small part of the method the Ministry could use to combat coronavirus entering New Zealand.
Currently, passengers arriving in New Zealand from China are proactively asked if they have flu-like symptoms. If so, a health check will be undertaken.
The most important thing that could be done was ensuring people at the border were well educated, Bloomfield said.
"It appears some people can be asymptomatic but be infected. Therefore, they may be harbouring the infection, or incubating it, but they may also be asymptomatic and infectious."
"So, border screening - of which there is a lot of focus - is a very small part of the efforts to ensure we are able to manage the possibility of a case here".
Tomorrow, all aspects of the Air New Zealand chartered flight to Wuhan would be revealed by the Ministry of Health.
New Zealand, Pacific Island and Australian citizens are the focal point of a Ministry of Foreign Affairs and Trade (MFAT) operation to evacuate those stranded in China.
The Air New Zealand chartered flight would land in Wuhan, the city where the virus started and which is currently under lockdown.
Passengers would be charged a nominal flat fee of $500 to board the flight, but first were required to fulfil a number of prerequisites.
"People who are granted access to this flight do not gain any extra immigration privileges into New Zealand," MFAT said in a statement.
"Anyone boarding the place must have the correct documentation to enter their final country of destination and they must pass the first health assessments."
The date when the flight would depart for Wuhan was yet to be determined but MFAT said it was working with Chinese authorities to get clearance.
Pre-flight assessment to ensure people were safe to travel would be undertaken by St John staff, Bloomfield said today.
There would also be measures in-flight to ensure crew and those on the flight were safe. However, he could not reveal what the Government's plan was once the flight had landed in New Zealand.
"As I say, the Government is expecting to make a further announcement on the whole package tomorrow."
Six people in total have been tested for coronavirus, including the one at Auckland City Hospital. None of them had the virus, however, the Ministry was still expecting coronavirus to spread to New Zealand.
Coronaviruses are part of a diverse family of viruses which include the common cold. This month, officials identified one called novel coronavirus, or 2019-nCoV.
Its symptoms - fever, coughing and difficulty breathing - are similar to a range of other illnesses such as influenza.
New Zealand's Ministry of Health said the risk of an ongoing outbreak in the country remained low, but it was actively monitoring the situation.
On its website, it encourages Kiwis to be proactive in their fight against infection by covering coughs and sneezes and using good hand hygiene.
They also encouraged people who had travelled within the past month to seek medical advice and contact Healthline on 0800 611 116.
Elsewhere, people in Auckland had started buying antiseptic sprays and liquids by the box as the world grapples with the coronavirus outbreak.
Countdown Meadowlands was bringing in extra stock of hand sanitisers, antiseptic liquids and antibacterial sprays - particularly Dettol.
Duty manager Kumar Than told The Weekend Herald its warehouse was sending extra stock for those items regularly now - something they had not seen before.
"All the shelves are getting empty very quickly," Than said.
"Those items like the hand sanitisers, Dettol, are selling very good, certainly after the coronavirus warning.
"We have online orders. Our staff doing online shopping, they're also seeing so many orders - especially sanitary items [like] Dettol and that kind of thing."