"On August 16, 2022, the most powerful cyber attack since the start of the Russian invasion occurred against Energoatom's website," the operator said on Telegram.
It "was attacked from Russian territory".
The Russian "popular cyber army" group used more than seven million internet bots to attack the website for three hours, Energoatom said.
But the assault "did not have a considerable impact on the work of the Energoatom website".
A Telegram channel called "popular cyber army" in Russian around midday called on its followers to attack the Ukrainian nuclear operator's website.
But by Tuesday evening it announced a change in plans, redirecting supporters to a new target — the Ukrainian Institute of National Remembrance, the website of which was sluggish.
Ukraine crisis latest - in pictures
The attack comes as tension flares over the Zaporizhzhia power plant in the south of the country, which Russian forces occupied in March, shortly after invading its pro-EU neighbour.
Russia and Ukraine have accused each other of shelling the installation, which is the largest in Europe, sparking fears of a nuclear accident.
Ukraine counted on four nuclear power stations to supply it with about half of its electricity supply before Russia's invasion on February 24.
Russian troops seize Chernobyl nuclear plant in Ukraine - video
Ukraine was the site of the world's worst nuclear accident in 1986, when the Chernobyl power station's reactor number four exploded.
The power station's three other reactors were successively closed down, with the latest shutting off in 2000.
Russian troops on the first day of the invasion seized the Chernobyl plant, occupying it and a highly radioactive exclusion zone around the complex for weeks.