The carrier is cancelling 40-50 flights daily for the next six weeks
Ryanair is seeking to reassure customers that their flights are unaffected, unless they receive an e-mail cancellation.
The carrier says: "We advise customers to check the e-mail address used to make their booking.
"Cancellation notices for flights cancelled up to and including Wednesday September 20th have been sent to affected customers and we will continue to send regular updates."
It comes as the airline confirmed it is to cancel up to 50 flights a day for the next six weeks.
It says this is due to several factors, including a backlog of holiday leave to pilots and cabin crew.
Ryanair says it is moving its holiday year from the current system of April to March to a calendar year of January to December from January 2018.
It says the backlog of crew leave must be allocated before December 31st this year to switch to a calendar leave year.
It says this is required by the Irish Aviation Authority (IAA).
Ryanair's Robin Kiely says: "We have operated a record schedule (and traffic numbers) during the peak summer months of July and August but must now allocate annual leave to pilots and cabin crew in September and October".
"We apologise sincerely to the small number of customers affected by these cancellations, and will be doing our utmost to arrange alternative flights and/or full refunds for them."
Affected customers will be contacted directly and offered alternative flights or full refunds.
The Irish Travel Agents Association (ITAA) has expressed "strong concern" over the cancellation of flights.
President of the ITAA Cormac Meehan says: "Given the dominant position of Ryanair in the Irish aviation market place, this action has caused severe problems for thousands of travellers travelling to and from Ireland.
"For many, holiday plans have been ruined by this action where the option to change holiday accommodation is not possible or can only be done at a significant cost."
"Ryanair’s actions will also have a considerable impact on route schedules internationally where many travellers are dependent on their Ryanair flight to connect to onward international flights.
"We are calling on Ryanair to publish a full list now of all flights they intend to cancel. The uncertainty of their actions is causing great unease amongst intending travellers."
The Commission for Aviation Regulation says it wants all passengers affected to be aware of their rights.
The commission says: "If you have been affected by the Ryanair programme of flight cancellations you are entitled to a choice of refund or rerouting.
"Compensation may also be payable depending on the notice period Ryanair has given you."
"Passengers who remain unclear about their entitlements as set out in EC Regulation 261/ 2004, or who have further queries in relation to same, should contact this office at firstname.lastname@example.org or on 1890-787-787 or + 353-1-6611700."
More information is available here