Tymur Tkachenko, head of the capital's military administration, said part of a residence had collapsed in the eastern Darnytskyi district.
"People are trapped under the rubble," Tkachenko wrote on Telegram "Emergency services are on their way to the site."
Tkachenko said buildings had sustained damage in other widely separated city districts including one where drone debris had fallen on the roof of a residential building.
Mayor Vitali Klitscho also reported damage to buildings throughout the capital, including debris that struck two buildings in a northern suburb, sparking a fire in a 12-storey block of flats.
Unofficial Telegram channels posted videos of parts of apartment buildings ablaze.
There were no immediate reports of casualties.
Ukraine's air force said Russian missiles had targeted other regions, including Kharkiv, Sumy and Chernihiv in northern Ukraine and the central region of Poltava. Russian drones and guided bombs had targeted other parts of the country, including eastern and southern regions.
On Wednesday, Russia unleashed a daytime drone attack on the country, targeting critical infrastructure in western regions and killing at least six people, officials said.
(Reporting by Ron Popeski; Editing by Christian Schmollinger and Kim Coghill)

epa12701912 The site of a Russian drone strike on a residential building in Kyiv, Ukraine, 03 February 2026, amid the Russian invasion. At least three people were injured in Kyiv as a result of the attack, according to the State Emergency Service of Ukraine (SES). Russia carried out another combined missile and drone strike across Ukraine, with the main targets being heating and electricity infrastructure during a severe frost, with temperatures below -20 degrees across the country. EPA/STRINGER