Explosions boomed across the sky on Wednesday morning as Ukraine's air force warned of incoming drones and Mayor Vitali Klitschko said air defences were repelling an enemy attack.
Two floors of a residential building in central Kyiv were partially destroyed in the strike, according to the State Emergency Service.
Two people were killed, it said.
Photos posted by the agency showed firefighters dousing a gutted corner of a building and rescuers helping elderly victims.
The National Bank of Ukraine said in a statement that one of its buildings nearby had been damaged by debris from a downed drone.
Debris also damaged a non-residential building in a different neighbourhood, authorities said.
"Even on New Year's Eve, Russia was only concerned about how to hurt Ukraine," President Volodymyr Zelenskiy said on social media in response to the strike.
Ukraine's military said it had shot down 63 out of 111 drones launched by Russia overnight across various regions of the country.
Another 46 had been downed by electronic jamming, it added.
Russia has carried out regular air strikes on Ukrainian towns and cities far behind the front line of its nearly three-year-old invasion, in which its troops are claiming village after village in a grinding march across eastern Ukraine.
On Tuesday, Russian forces fired 21 missiles at Kyiv and the northern Sumy region during an overnight strike, damaging buildings and infrastructure in the city of Shostka.
Separately on Wednesday, a 23-year-old volunteer worker was killed by Russian shelling in the southern front-line city of Kherson, city officials said.
