The 12-storey residential building was struck by a bomb that partially destroyed the first and third floors, Mayor Igor Terekhov wrote on Telegram.
“The number of injured keeps increasing. As of now, there are 25 of them,” he added.
Rescue efforts were under way for inhabitants trapped on the third floor.
The Ukrainian president’s chief of staff, Andriy Yermak, accused Russia of “deliberately hitting an apartment block”.
“The Russians are also attacking Kyiv with missiles,” he added.
Separately, Kyiv’s military office said that anti-missile air defences were operating in the capital.
A barrage of drones also struck Odessa and its suburbs in the south of the country, wounding at least two people, the region’s governor Oleg Kiper said.
Kyiv was targeted on Thursday by another “massive” Russian drone attack that wounded two people, damaged buildings and sparked fires in several districts, Ukrainian authorities said.
Russia has systematically targeted the capital with drone and missile barrages since the first day of its invasion launched nearly three years ago on February 24, 2022.
Ukrainian authorities have been seeking air defence systems from their allies to fend off Russian aerial attacks.