Europe's largest discount airline, which ordered 135 Max 200 models with the option for 75 more, had been expecting to receive its first five between April and June but now expects them to be flying by November.
For the airline, the addition of 737 Max jets had been projected to have added 1 million new passengers this summer alone.
"We're having a discussion with Boeing" about getting financial compensation for the delays, O'Leary said on "Squawk Box." "I don't need cash," he added, saying he wants movement on pricing. CFO Neil Sorahan told Reuters they plan to discuss "modest compensation."
Boeing's fleet of Maxes was grounded worldwide in March after the second crash in five months involving the model. The crashes in Indonesia and Ethiopia killed a combined 346 people. Anti-stall software is suspected in the crashes.
The Federal Aviation Administration has come under fire as people questioned the agency's oversight. The FAA's internal probe of the 737 Max approval process reportedly found senior agency officials failed to review crucial assessments of the flight-control system.
The 737 Max is touted for its extra seating room and ability to cut down on fuel usage, making the model more appealing for Ryanair, which is known for its small seats and costly amenities.
The Max seating would make it "ridiculously roomy," O'Leary said.
The company blamed the Max grounding and delivery delays for its profit warning. Shares of Ryanair that trade in the U.S. were down 1.6% Monday morning.
O'Leary said expects the 737 Max to be back in the air at airlines across the U.S. in June or July. "Ultimately, we have great confidence in Boeing and the FAA."
— Reuters contributed to this report.