The damage comes as temperatures drop below freezing and the capital Kyiv experiences its first winter snow.
One official in Kyiv warned that the city could face a "complete shutdown" of its power grid.
President Volodymyr Zelensky earlier said that 10 million Ukrainians have been left without power.
Engineers are racing to restore power as Ukraine endures Russian bombardment.
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"Unfortunately Russia continues to carry out missile strikes on Ukraine's civilian and critical infrastructure. Almost half of our energy system is disabled," Prime Minister Denys Shmyhal told a news conference on Friday.
Mykola Povoroznyk, deputy head of the Kyiv administration, said that the city is "preparing for different scenarios, including a complete shutdown".
He did not say what would happen in the event of the grid completely shutting down, but officials have said they are not considering evacuating any cities.
Ukraine's national grid operator Ukrenergo posted on Telegram: "The aggressor country has officially recognised that its goal is to destroy our energy infrastructure and leave Ukrainians without electricity and heat."
Snow in Lviv,
The first snow of winter has hit Ukraine, including the western city of Lviv
On Thursday, Russia hit more energy installations and civilian buildings less than two days after one of its heaviest bombardments yet.
This has been a recent Russian tactic following setbacks on the battlefield, and its impact is starting to be felt more acutely. Moscow says the attacks are a response to Kyiv's "unwillingness" to hold peace talks.
Those suffering power outages are mainly in the capital, Kyiv, the western city of Vinnytsia, the port city of Odesa in the south-west and Sumy in the north-east.
The government has urged people to save energy by reducing use of domestic appliances such as ovens, washing machines, electric kettles and irons.
In the recently liberated city of Kherson, the deputy head of Mr Zelensky's office posted photos of people using electricity in designated tents due to there still being no power, adding that the government hopes to have electricity restored in the city "by the end of this week".