Explosions reverberated through the city shortly after 1am, shortly after Ukraine's air force had warned on its Telegram channel that Russia might launch an Oreshnik intermediate-range ballistic missile.
Ukraine's air force did not immediately respond to a request for comment on whether an Oreshnik missile hit any target during the attack.
Kyiv Mayor Vitali Klitschko said on Telegram that one person was killed after a nine-story residential building in the capital's central district of Shevchenko was hit. Emergency services were on site to extinguish the blaze, he said.
In the same neighbourhood, several people were trapped inside an air raid shelter at a school after a strike blocked its entrance with debris, Klitschko said.
More people were believed to be stuck inside a shelter at a business centre in Shevchenko, the head of the city's military administration said.
According to the city military administration, 20 people were injured in the overnight attack.
Three more people were injured in the broader Kyiv region, according to the governor, Mykola Kalashnyk.
On Saturday, President Volodymyr Zelenskiy warned Russia was preparing a strike against Ukraine using the Oreshnik missile, citing intelligence from Ukraine, the US and Europe.
Russia has already attacked Ukraine twice with the Oreshnik, a missile Russian President Vladimir Putin has boasted is impossible to intercept because of its reported velocity of more than 10 times the speed of sound.
Zelenskiy's warning came after Putin ordered his military to prepare options for retaliation against Ukraine for a drone strike on a student dorm in the Russian-occupied Luhansk region of eastern Ukraine on Friday.
Ukraine's military denied the accusations and said it had targeted a Russian drone command unit.
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