The airline is cancelling some flights on high-frequency routes from Ireland to London, and other United Kingdom destinations including Glasgow, Manchester and Newcastle.
Fórsa said strike action is a "last resort", adding: "They know it's bad news for passengers, for the airline, for Ireland's economy and tourism sector and for pilots themselves".
The Irish Airline Pilots Association has advised its members to get financial advice "due to the likelihood of industrial action continuing over a prolonged period".
Ryanair said customers on these routes could transfer "readily" to other flights.
IALPA claims a ballot of pilots directly employed by Ryanair resulted in 99% voting in favour of a strike, but Ryanair claims this only represents 27% of its employees in the Republic of Ireland.
Management and unions are due to meet on Wednesday at Dublin Airport in a bid to minimise disruption.
If you are one of the unlucky people who've had their flight cancelled the airline would have notified you already.
Pilots opted or industrial action after the airline failed to address their concerns over seniority, annual leave and promotions.
Cabin crew in Italy will go on strike for 24-hours on 25 July, while crew in Spain, Portugal and Belgium will strike for 48 hours on 25-26 July.
'All customers on these flights have received text and email notification of these cancellations earlier today and our Customer Service teams are assisting them with refunds, free transfers to alternative flights on Thurs, or Wed, Fri and Saturday.
The airline said it sent proposals to Forsa but the union said they were not the basis of a settlement.
Ryanair have expressed on their social channels that they have been contacting Fórsa in an attempt to halt planned strike action but as it stands no definitive agreement has been reached.
The strike comes in peak tourist season, following repeated strikes by air traffic controllers across Europe in June.