The attack came as Russian forces said they had captured two more villages in eastern and southern Ukraine, where Kyiv's outnumbered forces have steadily lost ground to Moscow.
President Volodymyr Zelensky, in a social media statement, said Russian forces had targeted civilians and energy facilities in nine regions and the capital Kyiv with the strikes.
"We count on America, Europe, and the G7 countries not to ignore Moscow's intent to destroy everything," Zelensky said, calling for more sanctions to pressure Russia to end its invasion.
DTEK, Ukraine's largest private energy company, said power plants were damaged in various regions, without specifying which ones.
Its CEO Maxim Timchenko called it a "bad blow in our efforts to keep power flowing this winter."
National electricity operator Ukrenergo said the attack had put its energy system in a "difficult situation" and that power outages would last across the country until late Thursday.
"Round-the-clock" blackouts would also be in introduced in all regions on Friday, Ukrenergo added.
In the western region of Lviv, which borders NATO and EU member Poland, the regional governor said two energy facilities were hit.
The energy ministry said a "significant number of consumers" were cut off from electricity supplies as a result of the attacks, without giving figures.
The Russian Defence ministry said it had launched a "massive" missile and drone attack on Ukrainian military-industrial sites, energy infrastructure and airbases.
The Kremlin has attacked Ukrainian power infrastructure each winter since invading in 2022, forcing Kyiv to impose electricity restrictions and import energy from abroad.
- Russia captures villages -
The Russian barrage consisted of 52 missiles and 653 drones, the Ukrainian air force said, adding that it had downed 623 air targets.
In the southeastern city of Zaporizhzhia, the regional military administration chief said two people were killed and 23 were wounded, including six children.
An AFP journalist saw a residential building gutted in the attack and rescue workers clearing debris while residents surveyed the destruction.
In the central Vinnytsia region, a seven-year-old girl died of injuries from an attack and four more people were wounded, a local official said.
Prosecutors in the Kherson region said one person was killed in the morning as Russia attacked settlements "using artillery, mortar weapons, and drones of various types."
AFP journalists in Kyiv heard Russian drones buzzing over the capital overnight.
Three people were also killed after Russia fired MLRS rockets at Sloviansk in the eastern Donetsk region, regional police said.
Russia's defence ministry meanwhile said it had downed 170 Ukrainian drones overnight, including 48 in Bryansk region, which borders Ukraine, and nine in Moscow region which surrounds the capital.
And it said its forces had wrested control of Sadove in the northeastern Kharkiv region and Krasnogirske in Zaporizhzhia region, which the Kremlin claims is part of Russia.
Moscow has kept up a near-constant barrage of drone and missile attacks as it grinds on with the invasion it launched in February 2022.
Ukraine has increasingly responded with its own strikes targeting Russian oil refineries and other energy infrastructure.
US President Donald Trump has been trying to secure a peace deal since he returned to the White House in January, but talks have made little progress.
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