Chernobyl was the site of the worst nuclear accident in history in 1986 (File)
The resolution passed by the International Atomic Energy Agency (IAEA) board of governors also "deplores the Russian Federation's actions in Ukraine, including forcefully seizing control of nuclear facilities and other violent actions", according to a copy of the text sent to AFP.
The motion passed by a large majority on the 35-member board, with 28 countries in favour and only Russia and China voting against, a diplomatic source said.
India, Pakistan, Senegal, South Africa and Vietnam abstained, according to the source.
The Chinese ambassador to the UN in Vienna, Wang Qun, said the resolution had "obviously gone beyond the IAEA's mandate by introducing many politicised elements".
His Russian counterpart, Mikhail Ulyanov, said in a tweet the text "abuses (the) extremely important topic of nuclear safety and security for purely political purposes".
Ukraine has four active nuclear power plants, providing about half the country's electricity, as well as nuclear waste stores such as the one at Chernobyl.
On Monday, Grossi said he had received reports that Russian soldiers were close to the Zaporizhzhia nuclear plant in eastern Ukraine, the country's largest.
Poland and Canada had requested the meeting, which began on Wednesday, and tabled the resolution.
Chernobyl was the site, in 1986, of the worst nuclear accident in history. On February 26, it was taken over by Russian troops.
On Wednesday, IAEA Director General Rafael Grossi called for an immediate end to the conflict, saying this was "the best action to ensure the safety and security of Ukraine's nuclear facilities".