Ukrainian officials said a wave of Russian missiles hit several cities across the country.
The mayor of the Ukrainian capital, Kiev, Vitaliy Klitschko, said several explosions in the capital had killed at least one person and damaged a hotel.
The attacks came two days after Russia carried out one of the largest airstrikes since the war began.
Ukrainian President Volodymyr Zelensky has warned that Russia may launch more attacks to make Ukrainians “celebrate the New Year in the dark”.
Russia has targeted Ukraine’s energy sector in recent months, destroying power plants and plunging millions into darkness during the country’s harsh winter.
Several top Ukrainian officials hinted at the attacks on social media, saying Russia would fail to spoil their celebrations.
Mykolaiv governor Vitaly Kim said on Facebook that there were reports of Russian missile launches.
“The occupiers decided to try and ruin our day,” he said.
In Kiev, people rushed to shelters as sirens sounded.
Rescuers have been dispatched to many areas affected by the blasts.
Deputy head of the presidential office, Kyrilo Tymoshenko, said on Telegram that one of the hotels was damaged.
Air defense was activated throughout the country.
A Ukrainian official said a drone strike injured two people in the western city of Khmelnytskyi.
The attacks came as Russian President Vladimir Putin accused the West of “provoking” Moscow into launching its February 24 invasion of Ukraine.
“The West lied about peace. It was preparing aggression… Now they are cynically taking advantage of Ukraine and its people to weaken and divide Russia,” Putin said in a provocative New Year’s speech.
Ukraine and the West reject Russia’s accusations of initiating aggression.
The Ukrainian government has appealed to Western leaders to equip it with additional air defenses, and US President Joe Biden recently agreed to equip it with the US-made Patriot missile defense system.
Moscow rejected Ukraine’s proposal to start peace talks in 2023, saying “Kyiv is not yet ready for real peace talks”.