Aer Lingus has extended the period for passengers to change bookings free of charge.
Passengers can now cancel flights they have booked from Tuesday until Friday. The airline expects widespread disruption to its operations this week.
Negotiations attempting to resolve a row with pilots over working rotas collapsed on Saturday.
Flights to and from Belfast are unaffected but the dispute will affect flights out of Dublin and Cork.
Aer Lingus chief executive Christoph Muller said it could lead to a full cancellation of operations from Tuesday.
Travellers from Northern Ireland intending to use Dublin Airport next week for onward connecting flights are advised to check the Aer Lingus website.
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