At least 11 people were injured as emergency crews responded to multiple strikes, Mayor Vitali Klitschko said in a statement.
Five people needed hospital treatment, including one man in critical condition and a pregnant woman, after a series of powerful explosions sounded in the city and air defences were activated.
The attack on the capital was ongoing, officials said, urging residents to remain in shelters until the air raid alert is lifted.
City authorities warned that power and water outages are possible.
In the Darnytskyi district, debris landed in the yard of a residential building and on the grounds of an educational facility.
A car caught fire after being hit by falling fragments.
Debris damaged three apartment buildings, a private household and caused a fire in the Dniprovskyi district.
Five residential buildings and a non-residential structure were damaged in the Podilskyi district.
In the Shevchenkivskyi district, falling debris sparked a fire in an open area near a medical facility and inside a nonresidential building.
There were also fires burning in four other districts.
In the Kyiv region, Russian strikes damaged critical infrastructure and private homes, injuring at least one civilian, regional head Mykola Kalashnyk said.
A 55-year-old man in Bila Tserkva suffered thermal burns and was transported to hospital, he said.
Fires also broke out in private houses in the capital's suburbs.
The strike came as European Union officials warned this week that Ukraine must continue to crack down on corruption following a major graft scandal that has put top nuclear energy officials under scrutiny.
But they also offered assurances that aid will continue to flow as Kyiv strains to hold back Russia's invasion.
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