There is also disruption to Cork Airport's flights.
Passengers are being advised to consult with their airline's website for the latest information on their flights.
Some ferries have also been disrupted due to the adverse weather conditions.
Irish Ferries say that Dublin to Holyhead 8.45am and 2.30pm and Holyhead to Dublin 11.50am and 5.15pm are either cancelled or in doubt.
Stena Line has said that the 9am Rosslare to Fishguard has been cancelled but that passengers will be transferred to Pembroke Dock instead.
Flights have been diverted to Shannon Airport with approximately three from Cork and nine from Dublin.
Shannon Airport has said that passengers flying from the airport will not be affected by diversions this morning.
Some flights have also been diverted to Belfast, Liverpool and Edinburgh airports.
Aer Lingus has said that up to 18 of this morning's flights may be cancelled or significantly delayed.
Six Ryanair flights to the UK have been cancelled. Five from Dublin Airport and one from Cork Airport.
Met Éireann has issued a Gale Warning that west to to southwest gales or strong gales will continue overnight along all Irish coasts with occasional storm force winds on the Irish Sea.