Russian officials said several power and energy facilities were targeted in the overnight strikes.
The fire at the nuclear facility was quickly extinguished with no injuries reported, according to the plant's press service.
While the attack damaged a transformer, radiation levels remained within normal ranges.
The United Nations' nuclear watchdog said it was aware of media reports that a transformer at the plants had caught fire "due to military activity," but hadn't received independent confirmation.
It said its director-general, Rafael Mariano Grossi, said that "every nuclear facility must be protected at all times".
Ukraine did not immediately comment on the alleged attack.
Firefighters also responded to a blaze at the port of Ust-Luga in Russia's Leningrad region, home to a major fuel export terminal.
The regional governor said approximately 10 Ukrainian drones were shot down, with debris igniting the fire.
Russia's Defence Ministry claimed its air defences intercepted 95 Ukrainian drones over Russian territory overnight into Sunday.
Russia fired 72 drones and decoys, along with a cruise missile, into Ukraine overnight into Sunday, Ukraine's air force said.
Of these, 48 drones were shot down or jammed.
The incidents occurred as Ukraine marked independence day, commemorating its 1991 declaration of breaking away from the Soviet Union.
President Volodymyr Zelenskiy delivered remarks in a video address from Kyiv's Independence Square, emphasising the nation's resolve.
"We are building a Ukraine that will have enough strength and power to live in security and peace," Zelenskiy said, calling for a just peace.
"What our future will be is up to us alone," he said, in a nod to the US–Russia summit in Alaska earlier in August, which many feared would leave Ukrainian and European interests sidelined.
"And the world knows this. And the world respects this. It respects Ukraine. It perceives Ukraine as an equal," he said.
Canadian Prime Minister Mark Carney arrived in Kyiv on Sunday morning for meetings with Zelenskiy.
"On this special day — Ukraine's Independence Day — it is especially important for us to feel the support of our friends. And Canada has always stood by our side," wrote Andriy Yermak, Zelenskiy's chief of staff.
In a joint press conference with Zelenskiy, Carney announced that Canada will invest 2 billion Canadian dollars ($A2.3 billion) in new military assistance for Ukraine to bolster its army and provide urgently needed weapons.
Zelenskiy said the two leaders were considering the presence of Canadian forces on the ground in Ukraine as part of a reassurance force.
Norway announced significant new military aid on Sunday, pledging about 7 billion kroner ($A1.1 billion) for air defence systems.
Prime Minister Jonas Gahr Store said Norway and Germany are jointly funding two Patriot systems, including missiles, with Norway also helping procure air defence radar.
Pope Leo XIV prayed on Sunday for peace in Ukraine as he marked the country's independence day with a special appeal during his weekly noon blessing.
He said the faithful were joining Ukrainians, "asking that the Lord give peace to their martyred country".
Leo also sent a telegram to Zelenskiy, which the Ukrainian leader posted on X, along with similar congratulatory notes from other world leaders.
Russia's Defence Ministry said on Sunday that 146 Russian servicemen had been returned from Ukraine, in exchange for the same number of Ukrainian servicemen.
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