The resolution at the board of the governors of the International Atomic Energy Agency (IAEA) 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.
A diplomatic source said the resolution passed by a large majority, with 28 countries in favour and only Russia and China voting against.
Senegal, South Africa, Vietnam, Pakistan and India abstained, according to the source.
Ukraine has four active nuclear power plants, providing about half the country's electricity, as well as stores of nuclear waste such as the one at Chernobyl.
Poland and Canada had requested the meeting, which began on Wednesday, and proposed the resolution.
Chernobyl was the site of the worst nuclear accident in history in 1986 and last Thursday the site fell to Russian troops.
On Wednesday, IAEA Director General Rafael Grossi called for an immediate end to the conflict at the meeting, saying this was "the best action to ensure the safety and security of Ukraine's nuclear facilities".