"As a result of debris falling in Shevchenkivskyi district of Kyiv... 2 people died, according to initial reports," Sergiy Popko, head of the Kyiv City Military Administration, wrote on Telegram.
Another person was injured and was being given medical assistance, he said.
Kyiv mayor Vitali Klitschko wrote on Telegram that "two dead men were found" in a non-residential building in Shevchenkivskyi district.
He did not specify how they died nor whether they were the same two reported by the city's military administration.
The regional military administration had earlier warned of a missile attack and said air defences were operating.
An AFP reporter heard at least three loud explosions in the centre of Kyiv around 5am local time (0200 GMT).
Emergency services had also deployed to the southern Darnytskyi district, where debris had fallen onto a commercial building, Popko wrote on Telegram.
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