Timur Tkachenko, head of the capital's military administration, said on Sunday the overnight attack occurred in the Holosiivskyi district, just outside the city centre.
"The building has been partly destroyed and there is a fire. Rescue teams are at the site," Tkachenko said.
Tkachenko earlier said there were 10 drones above the city and more coming.
Reuters witnesses heard anti-aircraft units in operation around the city.
Ukrainian President Volodymyr Zelenskiy said it was "a large-scale and vile Russian attack".
"Russia fills each day with horror and murder, it's simply dragging out the war. All of this demands a response — a strong response from the United States, from Europe, and from everyone in the world who wants this war to end," he wrote on X.
Earlier on Saturday the Russian Defence Ministry said its troops were advancing slowly on the eastern front and had captured two settlements in Donetsk region as well as one in Ukraine's northern region of Sumy.
Since their failed advance on Kyiv in the first weeks of the war, Russian forces have focused on capturing the Donbas in the east, made up of the Donetsk and Luhansk regions.
In recent months, Moscow has also tried to advance in Sumy region, particularly after Russia's military said it had ousted Ukrainian troops from the Russian border region of Kursk.
A Russian Defence Ministry statement said its forces had captured the village of Stupochky in Donetsk region, east of Kostiantynivka, a town under recent Russian pressure.
It also said it had taken control of Otradne, a village further west along the 1,000-km front and announced the capture of Loknya, a village inside the Russian border in Sumy region.
The general staff of Ukraine's military acknowledged no such losses, referring to Otradne as one of several towns where Ukrainian troops had halted 18 frontline Russian attacks. It referred to Stupochky earlier this week as part of an area under Russian attack.
For months, Ukraine has reported attempts by Russian forces to occupy areas of Sumy region, but has never acknowledged the capture of any of them.
Meanwhile, Russia and Ukraine each exchanged 307 of their service personnel on the second day of an extended prisoner swap set to be the largest in the three-year war.
US President Donald Trump has suggested the swap could herald a new phase in stop-start efforts to negotiate a peace deal between Moscow and Kyiv. There should be 1000 prisoners released on each side over three days.
Saturday's swap was announced by Russia's defence ministry, as well as Zelenskiy.
"Tomorrow we expect more," Zelenskiy wrote.
"Our goal is to return each and every one of us from Russian captivity."
Reuters Television footage showed freed Ukrainian servicemen at a rendezvous point inside Ukraine coming off buses draped in blue and yellow national flags as waiting family members chanted: "Welcome!"
Women held up photos of missing servicemen and gathered around returnees to ask about their whereabouts.
Footage released by Zelenskiy's office showed one released serviceman in tears and being consoled by a woman in military uniform. People assigned to greet the soldiers handed them mobile phones, so they could call relatives.
"I can't believe I'm home," one man said.
20°C