A Shahed drone hit one of the buildings "at the centralized facility for the interim storage of spent nuclear fuel," President Volodymyr Zelenskyy said.
"An extremely critical infrastructure - and an extremely vicious Russian attack," he wrote on X, calling the attack intentional.
Radiation levels were not affected by last night's attack, according to the state nuclear power company Energoatom.
An area within a three-mile radius of the damaged Chernobyl nuclear power plant has been cordoned off since the 1986 meltdown.
Several people have been killed in Russian attacks elsewhere in Ukraine on Sunday, including three people in the Zaporizhia region and one person in Dnipropetrovsk.
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