"These measures will help ensure an adequate level of air safety by streamlining the transit procedure over Ukraine by the airlines, which disregard aviation rules in the closed airspace over (Crimea)," it said in a statement.
The airlines cross Ukrainian territory when flying to Bulgaria, Israel, Turkey, Egypt and Greece.
Ukraine's SAA did not say whether flights by Aeroflot and Transaero to Ukrainian cities would be affected.
Last week, Ukrainian Prime Minister Arseny Yatsenyuk said sanctions against Russia, which were backed by parliament on Thursday, could allow Ukraine to impose a "partial or full ban on the transit" of resources from Russia and on air flights and road traffic via Ukrainian territory.
On the Russian side, Prime Minister Dmitry Medvedev said last week that Moscow had decided to ban transit flights for Ukrainian airlines and that it was considering banning European and U.S. airlines as well in retaliation for sanctions.