Doctors say they will have to close entire clinics if people infect them or their staff.
Healthline staff took 2200 calls yesterday about coronavirus.
The phones are being answered 24-7, but some people are not heeding the advice to call.
An Auckland woman who tested positive for Covid-19 on Tuesday night after getting a swab from her GP had walked into the clinic and did not call ahead.
She also took domestic flights to and from Palmerston North before her case was confirmed.
Medical Association chair Kate Baddock said the woman did almost everything wrong in getting treatment.
"We all need to be very, very thoughtful about where we've been, who we've been in contact with, what symptoms we have and not just turn up to medical centres."
Dr Baddock said the risk to medical centre staff and other patients was huge.
"If a practice gets contaminated because somebody comes in with coronavirus and precautions aren't taken because they are at risk and haven't identified themselves as a risk to the practice, then there is a risk that every single person they've been in touch with may need to stand down for two weeks.
"A practice just has to close down and that's an incredibly costly thing to have to do in terms of healthcare."
Rural doctors are preparing to treat people in their cars to limit any possible spread of the illness.
Rural General Practice Network chair Dr Fiona Bolden said: "We try and triage people before they come in the door. We really don't want them coming into the practice and contaminating other people.
"So we will do as we had to do during the measles outbreak - try and see people in their cars and examine them there and make some kind of clinical decision on them from there."
Hamilton GP Rebekah Doran said her practice was looking at virtual consultations. She said a Skype-type of consultation would give doctors the chance to get a virtual assessment of how patients were breathing and how unwell they were looking, so it offered the chance for a better diagnosis than a phone conversation.
Patients who were very unwell would still need to come into the practice so doctors could take their temperatures and oxygen levels, Dr Dorren said.
Royal College of Practitioners medical director Dr Bryan Betty, said while he could understand people's concerns about coronavirus, it was important to keep things in perspective.
"Eighty to 90 percent of people who overseas get coronavirus get better - they recover. They get a mild to moderate cold flu-type illness.
"A lot of people get very few symptoms at all and on the whole they do get better so on the whole while people are anxious they need to be reassured by that fact."
