In both cases, the child had received their first vaccination dose at 15 months, but not the second, which is given at age 4.
The 4-year-old who was earlier diagnosed has passed the infectious stage and has returned to preschool.
Advice had been given to the two preschools involved and to parents.
"The advice urges parents who have not immunised their children to do so," Dr Brunton said.
"While we are continuing to trace the source of the disease, the key to preventing the spread is in the hands of the community."
Measles starts with a fever, runny nose, cough, red eyes and a sore throat. It's followed by a rash that spreads over the body.
It's highly contagious and spreads through the air through coughing or sneezing.
If you believe you or someone in your family has measles, phone your doctor before visiting a clinic.