Mayor Vitali Klitschko told residents to stay in air raid shelters. Kyiv city officials said air defences were at work and the air force reported that Russia had launched hypersonic missiles at the Kyiv region.
"Explosions in the city. Stay in shelters!" Klitschko wrote on the Telegram messaging app.
He said fragments of a downed missile had come down on the territory of a children's hospital in the city, but that there were no injuries or damage.
Reuters journalists in the capital could hear explosions but could not immediately verify the precise location.
National television broadcaster Suspilne reported explosions in the central and western regions of Vinnytsia and Khmelnytskyi. An official in Khmelnytskyi said air defences in the area were at work.