Rosatom's head Alexei Likhachev called the incident "deliberate" and said it left a hole in the wall of a turbine hall.
"This afternoon, a Ukrainian kamikaze combat drone struck the turbine hall building of Power Unit No. 6, resulting in a subsequent detonation," Likhachev said in a statement.
"The explosion caused no damage to the primary equipment; however, it tore a hole in the turbine hall wall."
Ukraine's military denied the Russian claims as "yet another propaganda ploy".
It said that the Ukrainian troops did not strike power unit No 6 at the Zaporizhzhia nuclear power plant.
"Ukrainian servicemen act strictly within the international humanitarian law and are fully aware of the consequences of any actions targeting nuclear facilities," the military said in a statement.
"At the relevant section of the front line, there was no active fighting during the incident and no weapons were used."
The Zaporizhzhia nuclear plant was captured by Russia in March 2022 and remains close to the frontline in the southeastern Ukrainian Zaporizhzhia region.
It has occasionally come under fire during the four-year-long war, raising fears of a nuclear accident at the facility.
"We are one step closer to an incident that will most likely affect even those who live far beyond the borders of Russia and Ukraine and still think they are completely safe," Likhachev said.
The Zaporizhzhia nuclear plant is not in service but it needs reliable power to cool its six shutdown reactors and spent fuel to avoid any catastrophic nuclear incidents.
The International Atomic Energy Agency has repeatedly expressed alarm about the nuclear plant.
Ukrainian President Volodymyr Zelenskiy reiterated his warning about a new large-scale wave of Russian air strikes on Saturday.
"The intelligence report regarding a possible large-scale attack remains valid," the president said in a video message a day after he initially sounded the alarm.
He urged Ukrainians not to ignore air raid sirens.
Although Ukrainian air defences are on standby, Zelenskiy acknowledged problems with foreign supplies for the country's defence against ballistic and cruise missiles.
Ukraine has been fighting a Russian invasion for more than four years with the assistance of allies.
The warring parties are making extensive use of drones and missiles against targets in the enemy's hinterland.
with AP and DPA
