The patient is the first to have met the criteria for a suspected case in New Zealand and the results would be available on Saturday.
Bloomfield said it was thought the person had come forward themselves - and he encouraged anyone else with symptoms to do the same and seek medical advice.
Meanwhile, urgent testing for the coronavirus can now be done in New Zealand, the Ministry of Health says.
But authorities say there is still no plan to step up screening of incoming travellers after the World Health Organisation declared the epidemic a public health emergency of international concern.
Currently there is only screening for direct flights from China.
To date, test samples from potential cases in New Zealand have been sent to Australia, but Director-General of Health Ashley Bloomfield on Friday confirmed local labs were now able to do the work themselves.
Results would be available within a few hours, he said.
In a separate statement, the Institute of Environmental Science and Research (ESR) said it would be running the test daily and results could be expected within 24 hours of getting a sample.
"To develop this test we had to source the right tools and material from overseas in a time of high demand and then validate the test locally through numerous experiments to ensure the quality of the result," ESR clinical virologist Erasmus Smit said.
The agency is also offering support to other labs trying to set up testing for the coronavirus.
Bloomfield said there had been about five cases checked in New Zealand but no one had met the definition of a suspected or confirmed case. A handful were expected to be checked each day.
Virus Spread
Meanwhile, the WHO this morning declared the coronavirus outbreak a public health emergency of international concern.
Responding to the decision on Friday, Bloomfield told reporters the WHO's directions vindicated the local response so far and there was no plan for any changes to safety measures.
"What it does is emphasises and endorses the actions New Zealand has taken to date," he said.
There would be no urgent changes to how flights arriving from areas hit by the outbreak were being screened or travel restrictions.
But National Party health spokesman Michael Woodhouse said more needed to be done.
"[Screening] needs to be broadened to include all passengers who have travelled from or through affected countries," he said.
"Another step the Government should be seriously considering is screening passengers arriving on cruise ships who have been through affected countries."
Woodhouse has also called for more health staff at international airports beyond Auckland and Christchurch, and for tourism companies and accommodation providers to be contacted and given resource to help detect and possible cases. China says the death toll from the virus has reached 170, while there have been 82 infections reported in 18 countries outside China.
Health officials have reported the first US case of person-to-person spread of the new virus from China.
