Chernobyl was the site of the world's worst civil nuclear catastrophe when one of its four reactors exploded in 1986. That reactor is now enveloped by a protective shelter, known as a sarcophagus, to contain the lingering radiation.
The Russian drone struck the shelter of the destroyed power unit at the plant, causing a fire that has since been extinguished, he said.
"As of now, radiation levels have not increased and are being constantly monitored," Zelenskiy said, adding that an initial assessment had found significant damage.
"The only country in the world that attacks such sites, occupies nuclear power plants, and wages war without any regard for the consequences is today's Russia," he said.
There was no immediate comment from Russia, which has repeatedly denied targeting civilian facilities during its war in Ukraine.
The International Atomic Energy Agency said the strike occurred early Friday local time.
It said there was "no indication of a breach in the ... inner containment" shell.
The three-year Russia-Ukraine war has brought repeated warnings of dangers to Ukraine's four nuclear plants, especially at the Russian-occupied Zaporizhzhia nuclear power plant in southern Ukraine, which is Europe's biggest and one of the 10 largest in the world.
International Atomic Energy Agency chief Rafael Grossi said on X the strike and the recent increase in military activity near the Zaporizhzhia plant "underline persistent nuclear safety risks", adding that the IAEA remains "on high alert".
The IAEA said its personnel at the site responded within minutes of the strike, adding there were no casualties.
"Radiation levels inside and outside remain normal and stable," the agency said on X.
Andriy Yermak, the Ukrainian president's chief of staff, posted photographs of the shelter with what appeared to be a small fire near the top of its vast arch.
"The only country in the world that attacks such sites, occupies nuclear power plants, and wages war without any regard for the consequences is today's Russia," Zelenskiy said.
The shelter, known as the New Safe Confinement, is a hulking arch-shaped steel and concrete structure that was completed in 2019 to cover an earlier Soviet-built version, which had deteriorated.
According to the European Bank of Reconstruction and Development, the New Safe Confinement cost 1.5 billion euros ($A2.48 billion) and was financed by 45 donor countries and institutions.
Zelenskiy is in Munich on Friday to meet US Vice President JD Vance at a delicate diplomatic moment with US President Donald Trump pushing for rapid negotiations and an end to the war.
Yermak said the United States had contributed significant amounts of money and effort to building the New Safe Confinement structure.
"We will provide a lot of information to our American partners today about Russia's strikes on the Chernobyl nuclear power plant, about how they constantly launch drones over the Chernobyl zone, about the threat of shelter and nuclear security that they pose," Yermak wrote on Telegram.
"The atmosphere at the moment is that everyone is very angry at this news here in Munich. Not 'concerned', as is often the case, but really angry."
with PA
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