It had asked the CMA to review the ruling, which it claimed had been made because regulators were concerned the stake would discourage rivals from bidding for Aer Lingus.
A Ryanair spokesman said: "Ryanair has instructed its lawyers to appeal today's ridiculous decision to the Competition Appeal Tribunal, given that it is factually unsustainable and legally flawed as the IAG offer for Aer Lingus proceeds."
But the CMA said in a statement on Thursday that it believed there was no reason why it should change its decision to make Ryanair sell down its stake.
It said it believed the prospect of Ryanair having to reduce its stake had prompted IAG to bid for Aer Lingus.
Simon Polito, Chairman of the Ryanair/Aer Lingus inquiry group, said: "IAG's bid for Aer Lingus is dependent on securing Ryanair's agreement to sell its shareholding. This recent development illustrates that Ryanair can decide whether a bid for its major competitor on UK/Irish routes succeeds or fails."
"This concern was an important part of our decision to require Ryanair to reduce its shareholding. It's not good for competition when one company holds such an influence over the future of one of its major competitors.
"Although at this point Ryanair has yet to decide whether to sell its shares to IAG, we need to ensure that, whatever happens in relation to this particular transaction, Ryanair's ability to hold sway over Aer Lingus is removed."