But that will no longer be the case unless they fall into a high-risk group or their doctor advises it.
The high-risk group includes anyone who has recently:
• Had contact with an infected person. • Been overseas. • Had direct contact with someone who had been overseas. • Worked on an international aircraft or ship. • Worked at an airport or isolation facility.
Other people with a cold or flu symptom could still be tested but it will not be a requirement.
The move is expected to put an end to the huge demand for tests in some areas over the past week as the cold and flu season hits.
Northland GP Geoff Cunningham was so busy he ran out of swabs.
He was relieved to see the change.
"It would be unsustainable if we were to continue swabbing every minor respiratory tract infection," he said.
Leading public health doctor Nick Wilson said the change was the right thing to do because there was no evidence the virus was transmitting in the community.
"When you recognise that situation and the fact that we are going into winter when there is a lot more cold and flu, we do have to probably tighten these criteria so we're not wasting a lot of health worker time and resource on inappropriate testing," he said.
A GP registrar at Papakura Marae's health centre, Julea Dalley, said the clinic would most likely still remain very careful because they were near the airport and likely to see a lot of airport workers.
She welcomed the change, saying she hoped it would mean people who had been avoiding the clinic would make an appointment.
And the clinic still wanted people to turn up with sore throats, because of the risk of rheumatic fever, she said.
On Wednesday, people were waiting up to four hours for a Covid-19 test as winter ills combine with fears about new cases to create massive queues at community testing centres.
Drivers queuing outside the Panmure Langimiele health centre reported sore throats, runny noses and cold-like symptoms.
Many had been waiting between one and a half and two hours - but said getting tested was the right thing to do to stay Covid-19 free.
However, one woman said she had seen at least 15 cars leave in the 90 minutes she had been waiting.
The clinic's operations lead, Pauline Fuimaono Sanders, said wait times had jumped from between 15 to 30 minutes two weeks ago, to between two and four hours.
Yesterday was their busiest day yet, with 191 tests, up from the 30 to 40 tests they had been doing for most of alert level 1.
"I think people are getting worried ... I guess the main thing to remember is that the new cases are in quarantine hotels, not in the community.
"But I think because we had an increase in numbers it's just making people worried."
Director-general of health Dr Ashley Bloomfield reiterated on Wednesday there was no community transmission of Covid-19 - and said the increase in people presenting was partly because of winter ills and respiratory symptoms, and awareness of new cases over the past week.
"There will be thousands of tests being done every day and we can do up to 12,000 a day if necessary."