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The child had not yet received its first dose of the measles, mumps and rubella (MMR) vaccine.
It is thought the infant contracted the highly infectious disease while visiting Auckland, where there were 1238 confirmed measles cases as of 11.45am on Friday.
Members of the public do not need to be concerned, Canterbury District Health Board reported, as the baby had not been taken to public places.
Those who are not vaccinated should avoid travelling to Auckland, Canterbury medical officer of health Dr Alistair Humphrey said.
"It's important to make sure you're immunised two weeks before travelling. It takes up to two weeks for your immunity to develop.
"If you are unwell, telephone your General Practice team and explain the symptoms. It is now more important than ever that people who are unwell do not travel."
Meanwhile, a warning was issued for Jetstar customers who flew from Melbourne to Auckland on Monday after it was confirmed a passenger had measles.
They were not aware they were infected when they boarded the flight.
The flight, JQ217, departed Australia at 11.45pm and landed in Auckland at 5.20am on September 10, Auckland Regional Public Health Service (ARPHS) reported.
Anyone on board the flight, or in the airports' arrivals or departures areas, should watch out for measles symptoms, ARPHS warned.
Symptoms include a high fever, runny nose, cough and sore red eyes, ARPHS clinical director Dr Julia Peters said.
"A few days later a rash starts on the face and neck, then spreads to the rest of the body.
"It can take 7-14 days to start experiencing symptoms and you are most at risk if you're not immune to measles, either because you haven't been vaccinated or you haven't had the disease previously."
Those who were on the flight an unsure whether they're immune should talk to their doctor or call Healthline on 0800 611 116 for advice.
If symptoms start to develop, ARPHS said people should contact their doctor immediately - but be sure to call ahead to prevent infecting others.
What is measles?
Measles is a viral illness that causes a skin rash and fever. It is very contagious.
What are the symptoms of measles?
Symptoms usually begin to show about 10 to 14 days after infection with the virus.
The illness begins with fever, cough, runny nose and conjunctivitis (inflammation in the eyes), which lasts for 2-4 days.
It may be possible to see small white spots (Koplik spots) inside the mouth.
How long will it be before I know if I've caught measles?
It usually takes 10 to 14 days for someone who has caught measles to start showing symptoms.
If you have been near someone with measles, and don't know if you're immune, seek medical advice immediately and remain in quarantine at home.
When was the last outbreak of measles in New Zealand?
The last two major measles epidemics in New Zealand occurred in the 1990s, with thousands of cases, hundreds of hospitalisations and seven deaths.
Smaller outbreaks continue to occur, started when someone brings the disease back from an overseas trip.
Where can I seek advice or find out more about measles?
• Free phone Healthline on 0800 611 116 or visit:
• The Ministry of Health website – www.health.govt.nz
• The Immunisation Advisory Centre website – www.immune.org.nz (or free phone 0800 466 863)