NHS Lanarkshire said there is a concern of infection among those who are not vaccinated or not fully vaccinated, especially as the MMR vaccine uptake has been falling across the UK.
Measles is a severe condition which can lead to pneumonia and encephalitis (brain inflammation).
The health board said the best defence against the condition is having two doses of the MMR vaccine.
The first dose is offered between ages 12 to 13 months and the second at three years four months.
Even if these timelines are missed, the vaccine can be administered at any age.
Dr Henry Prempeh, consultant in Public Health Medicine, said: “Measles cases have increases significantly across other parts of the UK and Europe, and we would encourage parents with young children to get their child vaccinated.
“This will offer the protection against measles which can lead to more serious health issues.
“Given the current links to travel, it is also important your children are up to date with all their vaccinations before leaving the country.”
Those unsure of their vaccination status can consult their GP.
If not vaccinated or only partially, the GP can refer them to the NHS Lanarkshire vaccination team.
Lanarkshire residents can request their MMR vaccination by calling NHS Lanarkshire Vaccination helpline at 01698 687456, available Monday to Thursday between 9am and 5pm, and also on a Friday between 8.30am and 4.30pm.