The budget airline announced on Friday that it would cancel between 40 and 50 flights daily up until October, as it moves to reduce a backlog of holidays for staff.
Their website has detailed all the flights which are cancelled for today, with eight flights to and from Dublin included in the list.
The Dublin-based carrier insists it will offer refunds or alternative flight options to the "small number" of affected passengers. However, it is believed the move could affect up to 250,000 passengers.
Under EU law, thousands of passengers may be entitled to €250 compensation if the distance of their cancelled flight was 1,500km or less.
The Commission for Aviation Regulation stressed that affected passengers should be aware of their rights.
It said compensation in the event of a cancellation depended on the distance of the flight, and the reason for the cancellation.
It also depends on the 'notice period' given by the airline. If a carrier can prove that the cancellation was caused by an extraordinary circumstance, which could not have been avoided even if all reasonable measures were taken, no compensation is payable.
Examples of extraordinary circumstances may include weather conditions, air traffic control restrictions, security risks and industrial disputes that affect the operation of a schedule.
The Irish Travel Agents Association (ITAA) said it was deeply concerned over the cancellations at such short notice.