Canterbury Medical Officer of Health Dr Daniel Williams said advice had been given to parents at preschools the child attends.
"The advice urges parents who have not immunised their children to do so. People who choose not to vaccinate their children against infectious diseases are putting not only their own children at risk, but also other people's children," he said.
Last week it was also revealed a passenger on board a flight from Kuala Lumpur to Auckland had measles and was infectious.
Passengers on Malaysian Airlines Flight 131 on February 26 were urged to be vigilant for symptoms, and call their doctor before visiting if they felt unwell.
The initial symptoms of measles include a fever, running nose, cough and sore eyes.
Dr Turner told Newstalk ZB this morning that preventing a measles outbreak was very simple.
"It's a very straightforward issue: If we vaccinate enough people we will eliminate measles. If we don't vaccinate enough when measles gets introduced it spreads, particularly among the unvaccinated.
"She said the anti-vaccine movement was not widespread enough in New Zealand to have a major impact.
"The anti-vaccine movement is probably about 2 to 3 per cent and the rest of us make up for that by vaccinating our kids," Dr Turner said.
"The problem is historically we were not good at vaccinating for a whole lot of reasons."