Authorities said they successfully thwarted the Russian attack although wreckage from some of the drones damaged five buildings.
No casualties have been reported.
In a brief video statement, Ukrainian President Volodymyr Zelensky said the “terrorists” fired 13 Iranian-made drones and all were intercepted.
“All 13 were shot down by our Ukrainian air defence systems. Well done, I am proud.” Zelensky said in the address.
Such drones have been part of the firepower, along with rockets, missiles, shelling mortars and artillery, as Russia targets power stations, water facilities and other public utility sites.
The snow-covered capital remained largely calm after the attack, which occurred at around dawn. As the working day began, authorities sounded the all-clear.
The head of the Kyiv city administration, Serhii Popko, wrote on Telegram that the attempted strikes came in two waves. Wreckage from the intercepted drones damaged an administrative building and four residential buildings, he said.
A blast left the three-storey tax office building in the central Shevchenkyvskyi district with a gaping hole in the roof and blew out windows in parked cars and in a neighbouring building.
Clean-up crews were on site quickly to shovel away the rubble and roll out plastic sheeting to cover the blown-out windows in freezing temperatures.One man, unfazed, pushed his son on a swing set on a nearby playground as the crews did their work.
Anton Rudikov’s family was sleeping when they heard the sounds of an explosion nearby and smashing windows.“The children were frightened; the windows flew out,” said Mr Rudikov, who has daughters aged 13 and 18.
“What else can I say?”
Local residents told Associated Press reporters they saw fragments from a drone which contained the words “For Ryazan”.
The Kremlin claims Ukraine was responsible for an attack on a military base in the Ryazan region of western Russia last week.
It came as officials said the US was poised to approve sending a Patriot missile battery to Ukraine, agreeing to an urgent request from Ukrainian leaders desperate for more robust weapons to shoot down incoming Russian missiles.
Meanwhile, the UK is providing training to scores of Ukrainian judges to carry out war crimes trials for Russian soldiers.
The first group of judges attended sessions at a secret location in the region last week, with more to follow in the coming months.
Attorney General Victoria Prentis told Sky News it would ensure perpetrators of atrocities can be prosecuted while the conflict goes on.