Russia has launched dozens of missiles at cities across Ukraine, officials there say.
Kyiv Mayor Vitaly Klischko said there had been several blasts in the city, causing damage and at least one death.
The attacks happened two days after Russia carried out one of the largest air strikes since the start of the war.
Ukraine President Volodymyr Zelensky had warned Russia could launch more attacks to make Ukrainians “celebrate the New Year in darkness”.
Several senior Ukrainian officials have alluded to the strikes in social media posts, saying that Russia would not succeed in ruining their celebrations.
Mykolaiv Governor Vitaly Kim said on Facebook that Russian missile launches had been reported.
“The occupiers have decided to try to spoil the day for us,” he said.
In Kyiv, people rushed to shelters as air raid sirens sounded.
Emergency workers were sent to three districts hit by explosions. Deputy presidential chief of staff Kyrylo Tymoshenko said on Telegram that a hotel had been damaged.
Air defence has been activated in regions across the country.
The attacks came as Russian President Vladimir Putin accused the West of “provoking” Moscow to launch its invasion of Ukraine.
In a combative New Year address, Mr Putin said: “The West lied about peace. It was preparing for aggression… and now they are cynically using Ukraine and its people to weaken and split Russia.”