Explosions reverberated through the city shortly after 1am local time after the air force announced a threat of an Oreshnik launch on its Telegram channel.
At least three people were injured and several residential buildings were damaged across the city early on Sunday, Kyiv Mayor Vitali Klitschko said on Telegram.
Debris was on fire on the premises of a school in the city centre, he added on Telegram.
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.
Ukraine's air force did not immediately respond to a request for comment on whether an Oreshnik missile hit any target.
Russia has already attacked Ukraine twice with the Oreshnik, a missile 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-controlled Luhansk region of eastern Ukraine.
Ukraine's military said it had targeted a Russian drone command unit.
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