As many as 60 Russian missiles had been spotted heading for targets in the country, said Vitaly Kim, governor of the Mykolaiv region in southern Ukraine.
Russia was "massively attacking," said Oleksiy Kuleba, governor of the Kyiv region, as the latest in a series of attacks on infrastructure across Ukraine since October unfolded.
The eastern city of Kharkiv, home to more than a million people, was left entirely without electricity as was the smaller city of Poltava in central Ukraine, the Oblenergo energy provider and Poltava Mayor Oleksandr Mamai said.
In the northern Sumy region, the attacks caused power outages, the governor there said, while in the south, officials said critical infrastructure in the Black Sea region of Odesa had been hit.
In Kryvyi Rih, also in the south, a residential building was hit, governor Oleksandr Vilkul said, adding that people could be trapped under the rubble. Several railway lines were left without power, the railway operator said.
Reuters heard explosions in the capital Kyiv but it was not clear if any were caused by missiles getting through air defences.
Earlier this week, Russia launched the first major drone attack on Kyiv in weeks. Two administrative buildings were hit but air defences largely repelled the attack, with 13 drones reportedly shot down.
Russia has attacked Ukrainian energy infrastructure almost weekly since October, causing power outages across the country even as its troops are bogged down in fighting to hold on to territory in the south and east, around a fifth of Ukraine.
Russia's TASS state news agency said at least eight people had been killed and 23 wounded by Ukrainian shelling in the village of Lantrativka in the Russia-controlled Luhansk region in eastern Ukraine.
Reuters was unable to immediately verify the latest battlefield accounts.
Ukrainian defence chiefs have predicted Russia will launch a new offensive early next year that could include a second attempt to take the capital Kyiv.
It could happen as soon as January, President Volodymyr Zelenskiy, General Valery Zaluzhniy and General Oleksandr Syrskiy were quoted as saying in interviews with The Economist magazine on Thursday.
The push could be launched from the eastern Donbas area, the south or neighboring Belarus, and could include another ground assault on Kyiv, the officials said.
Russia launched what it calls a "special military operation" to disarm and "denazify" its neighbor on 24 February, since when thousands have been killed, cities reduced to ruins and millions of people forced from their homes in what the West sees as an imperial-style land grab.
With the invasion now in its 10th month, European Union leaders agreed on Thursday to provide 18 billion euros in financing to Ukraine next year and hit Moscow with a ninth package of sanctions.
The measures designate nearly 200 more people and bar investment in Russia's mining industry, among other steps.
The US military announced it would expand training in Germany of Ukrainian military personnel with 500 troops a month, building on more than 15,000 Ukrainians trained by the United States and its allies since April.
The US Senate passed a bill for a record US$858 billion defence budget next year, authorising US$45 billion more than proposed by President Joe Biden. The bill, which Biden is expected to quickly sign into law, provides Ukraine with at least US$800 million in additional security assistance in 2023.
Both sides have ruled out a Christmas truce and there are currently no talks aimed at ending the conflict, Europe's largest since World War II.