The British Airline Pilots Association (BALPA) announced late Wednesday that 80% of its members who took part in a ballot had supported the industrial action after negotiations with Ryanair reached an impasse.
The pilots are scheduled to strike for two days starting August 22, and again from September 2 to September 4.
"Ryanair management cannot understand how to go about working with us constructively," the union said in a statement. "No pilot wants to spoil the public's travel plans but at the moment it seems we have no choice."
Europe's biggest low-cost airline first recognized unions in December 2017, but it has been slow to reach agreements with its workers in some key markets.
Ryanair (RYAAY) called for talks to resume. It said less than half of its UK pilots are members of the union.
"BALPA have no mandate to disrupt our customers holidays and flights, particularly at a time when UK pilots are facing job losses due to the Boeing MAX delivery delays, and the threat of a no deal Brexit," the airline said in a statement.
The Irish carrier said last month that it was planning to cut back operations at some airports in Europe and abandon others entirely because regulators may not return the grounded 737 Max to service until December.
Ryanair had planned its flight schedule based on the delivery of 58 of the 737 Max aircraft by summer 2020. The airline, which can take delivery of up to eight aircraft per month, now expects to receive only 30.
The company slashed its expected passenger growth rate for next summer from 7% to 3% as a result of the delay. That means it will fly 5 million fewer passengers than expected in the year to March 2021.
Its 2019 performance could be further compromised if Britain crashes out of the European Union on October 31 without a deal to protect trade.
Analysts at Bernstein Research said they expected the Ryanair pilot strike to go ahead, and suggested the move could encourage unions in other countries to take similar action.
Shares in Ryanair were little changed on Thursday.
British Airways pilots voted last month to strike for the first time since the 1970s. BALPA has said it's committed to finding a negotiated solution to that dispute, and strike dates have not yet been set.