Sime told Morning Report, she was “very worried” about the spread.
This week’s cases were unrelated to a previous outbreak in Northland and a single case in Queenstown last month.
“Three of these cases are not linked to overseas travel which means there is a very strong likelihood of undetected cases in the community,” Sime said.
“What it means is there was at least one infectious case that has infected our three cases which could have spread it to others in the community.”
Sime said one of the infected children was school-aged and it was expected any locations of interest would be published as soon as possible today.
The disease is highly contagious and can cause serious and potentially long-term health problems.
Simes warned the public to be vigilant for symptoms of measles, including a cough, runny nose, high fever and red, sore eyes.
During the last measles epidemic, in 2019, about one in three people needed hospital care.
Sime said the disease could affect a person’s immune system for months or even years afterwards.
The best prevention, she said, was getting vaccinated.
“It’s very preventable through vaccination. Our vaccination rates are too low, we need to be at 95% to stop measles spreading.”
– RNZ