The move, which the airline said could still be reversed, comes months after Ryanair set up a base at Budapest following the collapse of Hungary's national airline Malev.
Chief Executive Michael O'Leary said the cuts would be made after airport operator Hochtief HOTGn.DE raised its user charges.
He criticised what he called an "even crazier" decision by the Hungarian aviation authority to raise air traffic control charges by 20 percent next year.
"The strange logic of Budapest (airport) and Hochtief seems to be, 'we have less traffic so we charge the existing traffic more'. That recipe is doomed to failure," O'Leary told reporters at a news conference in the Hungarian capital.
A Hochtief spokesman said there was nothing surprising about the price increase by the company running the facility, Budapest Airport Zrt, in which it has a 49.7 percent stake.
"It is very surprising Ryanair is addressing Hochtief, as we do not own the majority. We own 49 percent," Hochtief spokesman Christian Gerhardus said. "Budapest took the decision to raise the prices like every other normal company. That's it."
He said a reduction in the number of flights offered by Ryanair was expected as part of the winter flight schedule and that such cuts are not unusual for low-cost airlines.
"REFUGEE CAMP"
O'Leary said Budapest Airport had not provided the efficient facilities agreed upon in February. He took special issue with tents recently set up for boarding passengers on the tarmac.
"It is important that it is not just costs. We have also facilities problems with the airport, not least of which is the new tented village, (which is) somewhat reminiscent of a U.N. refugee camp at the airport," O'Leary said.
"If you fix all this crap we'll go back to growing, but if you don't fix this crap, then we are going to cut traffic and you'll be the loser," he said.
Financial problems among flag carriers in Europe offer a major growth opportunity for Ryanair. The airline moved into Budapest in February with five aircraft based there now.
It plans to cut that to three and close 10 of the 30 routes operated from Budapest from January 10.
The airline said this would result in a 40 percent fall in Ryanair's passenger traffic at the airport to 1.2 million per year and would lead to the loss of 800 local jobs.
Ryanair has previously cut routes from other airports where it has wanted lower airport charges but the company is not considering pulling out of Hungary altogether, O'Leary said.
Ryanair said its flights from Budapest would drop by 110 to less than 170 per week as it would also be cutting the frequency of its flights on nine of the 20 remaining routes. (Additional reporting by Matthias Inverardi; Editing by Tom Pfeiffer)
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