The HSE said it has already been monitoring "anti-vaxxer" comments on social media ahead of UK Prime Minister Boris Johnson's new crackdown on misleading messages about life-saving jabs.
Mr Johnson is ordering urgent action to ensure that children and young people in the UK are protected against measles.
The disease can be stopped through two doses of the MMR vaccine, but immunisation rates have been falling in several countries.
In the first quarter of 2019, there were 231 confirmed cases in the UK. Ireland recorded 55 measles cases to mid-August this year, a slight drop from 65 in 2018.
Take-up of the MMR vaccine in this country is best in the west and midlands, with several areas exceeding the 95pc coverage target at two years of age.
But other parts of the country are not meeting the target, with rates among children at this age in west Co Cork and west Co Wicklow at only 85pc to 89pc.
Nationally, MMR vaccination rates are at 92pc, which exposes Ireland to ongoing risk of measles outbreaks.
Mr Johnson announced that GPs in the UK are being asked to promote catch-up vaccinations for children who may have missed out on having both doses.
Social media companies are being urged to quash misleading anti-vaccine messages.
The firms will be invited to a summit to explore how they can better promote accurate vaccination information.
The HSE said yesterday it is already taking several actions including monitoring of national and local social and mainstream media for anti-vaccination activity.
A spokeswoman said it is tailoring messages on HSE social media accounts promoting vaccination and on its National Immunisation Office website, which is World Health Organisation approved.
Other actions include providing spokespeople and experts on vaccination and responding to vaccine-related issues in the media.
There are media campaigns to promote vaccination such as the HPV jab as well as work with other stakeholders to promote vaccination, including the Department of Education in the schools' immunisation programme.
GPs are also offered training in vaccination while the Department of Health is establishing a vaccine alliance.
Uptake of the MMR vaccine in the UK is 94.9pc for the first dose, but this drops to 87.4pc for the second dose, which falls short of the 95pc needed to produce herd immunity.
Health Minister Simon Harris looked at the possibility of mandatory vaccination but this will not go ahead.