Two cases are in Manawatū, one in Nelson and one in Auckland that was linked to overseas travel.
Health NZ's public health medicine specialist Dr Sharon Sime, said there was potential for other cases and officials were investigating locations of interest.
She said there was a risk of measles outbreaks if it was spreading in the community.
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 out 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 on Wednesday.
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 was getting vaccinated, she said.
"It's very preventable through vaccination. Our vaccination rates are too low, we need to be at 95 percent to stop measles spreading."
