It said the best protection from the disease was for people to have two doses (measles, mumps and rubella) vaccinations.
But it was standard practice between 1969 and 1990 for doctors to give just one, leaving a number of people at risk.
Canterbury Medical Officer of Health, Dr Ramon Pink said measles was now "in widespread circulation" and those who weren't fully immune could be exposed to the risk of infection.
"Immunisation is the only sure way to avoid getting measles," Pink said.
"Those aged between 29 and 50 will only have had one measles vaccination and are not considered immune."
The DHB has told medical centres in the region that extra supplies of the vaccine were being delivered, with 18,000 doses expected to be available in practices from Wednesday.
"Given their higher risk, our focus over the short term is to provide MMR immunisations to those under 29 years who are not fully vaccinated," Pink said.
"People between the ages of 29 and 50 can expect to get a measles vaccine from their general practice in a week or two."
People who think they might have been exposed to measles or have symptoms are asked to contact their general practice first.