Health officials say the person got the disease after having contact with a patient who had measles.
Measles symptoms include rash, high fever, cough, runny nose and red, watery eyes.
Officials are recommending anyone who visited several locations in Somerset County between March 6 and 12 to contact a doctor to discuss their potential exposure to measles.
The locations include Somerset Medical Center, Steeplechase Cancer Center, Somerset County Human Services Building, Somerset County Administration Building and several retail establishments in Bridgewater.
Detailed information is available on the state Health Department website.