"Today, we want to warn every airline that uses Russian airspace, every insurer, everyone who still uses key Russian airports: the Russian sky is becoming completely dangerous," Zelenskiy said in his nightly video address.
Ukraine poses no threat to civil aviation, he said, "but there will be drones in Russia's skies and due notice must be taken".
"Although Russian authorities are not properly announcing it, Russian airspace will effectively be closing. The war started by Russia is closing its own skies," Zelenskiy added.
Russia has stepped up its air attacks on Kyiv and other cities in recent weeks, with the latest Russian strike killing 12 people and injuring many more, the sixth straight day of intense assaults on the Ukrainian capital.
Ukraine has responded with frequent drone strikes on Russian targets, many associated with the country's oil industry as well as retail sites.
Russian President Vladimir Putin said on Tuesday that Zelenskiy's warning to airlines that Ukrainian drones would effectively shut down Russian airspace sounded like "state terrorism" and that Russia would find a way to respond.
Speaking at a news conference in Kyrgyzstan, Putin said it was not possible to negotiate with "terrorists".
But Putin also said that his country was open to "concrete" talks on settling the Ukraine conflict if new momentum could be injected.
He restated his confidence that Russian forces would prevail and Ukrainian forces would "crumble".
He said that the main challenge was drones but said that Russia was dealing with it.
