Pilots based in Portugal and Germany also plan industrial action.
The Irish airline, Europe's largest by passenger numbers, is still trying to recover from a damaging wave of flight cancellations caused by crew rostering problems.
Members voted overwhelmingly in support of strike action - 94 per cent in favour of industrial action.
Trade union the Irish Air Line Pilots' Association announced that a majority of its 84 Ryanair-employed members backed industrial action in a secret ballot which took place this weekend.
Numerous airline's pilots have joined unions following the cancellations, but Ryanair said it could legally decline to negotiate with them.
Ryanair has threatened to withdraw recent pay rises and other benefits from pilots who refuse to negotiate through the negotiating structures preferred by management.
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Vereinigung Cockpit said it won't strike during from the afternoon of December 23 through December 26, the height of the Christmas holiday travel period.
However, Connolly said pilots had been leaving the airline "in droves".
Ryanair said they will deal with any disruptions "if, or when they arise", and have apologised to customers in advance of any delays.
As part of a long-held policy, Ryanair has refused to engage with unions, or recognise a new European Employee Representative Council (EERC) that was established to represent Ryanair bases across the continent.
"Ryanair has received no notification of any industrial action by its Dublin pilots so we suspect this is more PR activity" by IALPA, the company said, referring to the union that is leading the drive in Ireland and already represents IAG SA-owned Aer Lingus. "While some disruption may occur, Ryanair believes this will largely be confined to a small group of pilots who are working their notice and will shortly leave Ryanair, so they don't care how much upset they cause colleagues or customers", the company's statement read.
"If any such action takes place, Ryanair will deal with it head on, but we will not deal with or recognize", the Cockpit union, it added in an emailed statement, "regardless of what action - if any - takes place".
The airline said last week it would "ignore" the Italian move, claiming staff rarely heeded calls to walk out.