The child went to a service at Our Lady of Victories Church at 6pm on February 3.
They were also at Nando's Restaurant in Sydenham between 5pm and 7pm on Waitangi Day and the Margaret Mahy Playground for a short period between 5pm and 10pm.
The child also attended two days of school and their medical practice.
Canterbury Medical Officer of Health, Dr Alistair Humphrey said the Community and Public Health team were working with the medical centre and school to ensure people who were exposed to the virus in those locations were contacted.
"We also need to warn those who were at the church, restaurant and the playground that they have been exposed.
"Anyone who was at that church service or at the Margaret Mahy Playground or Nando's in Sydenham after 5pm on Waitangi Day is potentially at risk.
"If you fall into that category and feel unwell, our advice is for you to stay at home and call your GP for medical advice. Staying at home is important as you may be contagious."
Humphrey said there was no risk to anyone who has visited the church, restaurant or playground at a different time.
He said the re-emergence of the virus was a timely reminder to people to ensure that they were fully immunised.
"These are the first cases of measles in Canterbury since May 2017. Community and Public Health staff are now working to contain any potential spread.
"The scheduled vaccinations are free from your general practice and some pharmacies. Measles is a very serious illness and we need to work together to ensure the South Island returns to its measles-free status."
The early symptoms of measles included fever, cough, runny nose, sore red eyes and white spots inside the mouth. After three to five days a rash may appear.
People are only considered immune if they have received two doses of MMR vaccine, have had a measles illness previously or were born before 1969.
