The strike significantly damaged a fuel-reception building metres away from where "large amounts of nuclear material" were stored, according to the International Atomic Energy Agency, which said it had been briefed by Ukraine.
Kyiv's state atomic agency Energoatom said no spent fuel had been stored in the building at the time of the attack.
A resulting fire was extinguished, and no injuries were reported.
Russia has not publicly commented on the alleged strike on the facility, which is located about 15km from the Chernobyl plant, the site of the world's worst nuclear disaster.
"An extremely critical infrastructure facility - and an extremely vile Russian strike," Zelenskiy wrote on X, adding that Russia had used a Shahed attack drone.
"As of now, there are no readings exceeding normal background radiation levels. But there is certainly an increase in Russia's brazenness, which long ago went off the charts."
In a statement, the International Atomic Energy Agency (IAEA) said a team would visit the site "to inspect the impact".
In February 2025, a Russian Shahed drone damaged a containment arch over the Chernobyl reactor that was destroyed in the April 1986 explosion and meltdown.
Russia, which regularly attacks Ukrainian cities and infrastructure with drones and missiles, denied responsibility.
Kyiv and Moscow have also traded accusations of attacking the Russian-occupied Zaporizhzhia Nuclear Power Plant in southeastern Ukraine, Europe's largest.
with Reuters
