The strikes, which would be the first in Ryanair's 32-year history, are being organised by pilots demanding an overhaul of the company's system of contracts and collective bargaining, which they say gives management too much power.
Pilots and ground crew in Italy are due to take action first with a four-hour strike on Friday, to be followed by a 24-hour stoppage by pilots in Ireland and Portugal on Dec. 20.
Pilots in Germany and Spain have said they are considering industrial action.
"Ryanair has been notified of threatened industrial action up to and including a 24-hour strike on Wednesday Dec. 20 next by a minority of our pilots in Ireland, Portugal, Germany, Italy and Spain. This may lead to some flight disruptions," a spokesman for the airline said in a statement on Thursday.
The company will publish contingency plans to minimise disruptions on Dec. 18, he said.
"We apologise sincerely to our customers... Rest assured that we will do everything we can to minimise disruption for our customers," the spokesman said.
Pilots at Europe's largest airline by passenger numbers have mobilised in the wake of the announcement of 20,000 flight cancellations by the Irish carrier, which it blamed on a lack of standby pilots due to a failure in its rostering following a rule change by Irish regulators.
Ryanair has denied claims by pilots that it has a pilot shortage.
Ryanair, which does not recognise trade unions, promised to "face down" the threatened strike.
Management has warned pilots in internal memos that pilots who take part in strike action may lose out on promotions and could cause the company to shift planes and jobs to lower-cost bases.
Portuguese union SPAC said in a statement that it "deeply regrets the failure by management to engage with the pilots' representatives in a meaningful manner."
It said its pilots had decided to strike because Ryanair was refusing to offer contracts under local rather than Irish law and to recognise the union's company council as its exclusive negotiating partner in Portugal.
Ryanair refuses to recognise unions, insisting instead on its own system of collective bargaining. Most pilots are hired on Irish contracts.
SPAC also demanded "a commitment to end the established culture of fear and bullying towards its (Ryanair's) crew." Ryanair denies there is any bullying at the airline and says it pilots have some of the best pay and conditions in the sector.
A spokesman for German union VC said it had not yet set a date for a strike in Germany.
(Reporting by Padraic Halpin and Conor Humphries; additional reporting by Victoria Bryan; Editing by Adrian Croft)
By Conor Humphries and Padraic Halpin