"The terrorists started this morning with 13 Shaheds," Ukrainian President Volodymyr Zelensky said, referring to the Iran-made weapons.
"All 13 were shot down" he added, urging residents to heed air raid sirens.
Explosions rang out over a central neighborhood in Kyiv in the early hours and AFP journalists later saw law enforcement and emergency service workers inspecting metal fragments at a snow-covered impact site.
Mayor Vitali Klitschko announced that explosions were heard in the central district of Shevchenkivsky and city officials said debris from the downed drones had damaged residential homes and an local administrative building.
No one was reported injured or killed.
Kyiv has been subjected to nearly ten months of air raid sirens and frequent aerial attacks since Russia invaded Ukraine in February and tried to capture the capital.
But the attacks have increased up since October when Russia began systematically targeting critical infrastructure in Ukraine in attacks that have disrupted electricity, water and heat to millions in Ukraine.
Foreign Minister Dmytro Kuleba called on Ukraine's allies to provide his country with more weapons to help it "fight through the winter" and sustain Kyiv's military advances.
In nearly 10 months of fighting, Russia has yet to fulfil any of its stated key goals in what it refers to as its "special military operation" in Ukraine, including seizing the capital or the eastern Donbas region.
The Moscow-installed leader of Ukraine's Donetsk region on Wednesday however called for Russia to widen its goals and annex two more areas of Ukraine, the Black Sea region of Odessa and Chernigiv in the north.