The company will cease operating from Cork to East Midlands Airport on 26 October and Glasgow Prestwick on 28 October.
Ryanair's Chief Executive Michael O'Leary said the company was making the decision due to an increase in the charges being imposed by the airport on those routes from 1 November.
However, Cork Airport management has rejected the claim by Ryanair that it has raised its fees by 20%. They say the airport has not raised its charges.
Mr O'Leary said that they had been in negotiation with the airport's management over the past two weeks and felt a deal was possible, but he claimed this was being blocked by the Dublin Airport Authority.
Mr O'Leary said the flights are barely profitable as it is and a 20% increase in airport charges reduces the airline's ability to offer cheap fares at a time of high oil prices.
Airport management said all airlines are eligible to apply for route support through the Route Support Scheme when introducing new destinations.
The Scheme operates over a five-year period and is based on a sliding scale with a 100% discount in year one.
In the second year of operation, the discount moves to 80% and so on over the five-year period of the scheme.
The closure of the two routes will mean a loss of 200,000 passengers going through the airport.
Mr O'Leary said the situation could be rescued if the Dublin Airport Authority changed its mind but as of now the two routes will finish in October.
The company runs four other routes out of Cork - to Stansted, Gatwick, Liverpool and Dublin and Michael O'Leary said these will not be affected.
These have been up and running for some time and profitable.
With regard to the decompression situation on board the Bristol/Barcelona flight yesterday, Michael O'Leary said the black box is being examined and it will take up to two weeks before they know what exactly happened.
