A Reuters witness heard a series of powerful explosions rock the capital overnight as the attack continued into Sunday morning and Ukraine's air force warned of a ballistic missile threat.
Fires broke out at a dormitory, a residential block and a supermarket, Kyiv Mayor Vitali Klitschko said on the Telegram app.
At least nine people were injured, and several non-residential buildings and warehouses were struck in the attack, while parked cars and office buildings were set on fire in several districts, Klitschko said.
Dozens of explosions, including from air defence systems, were heard across the centre of the city, according to a reporter at the scene.
Ukraine has been fighting Russia's full-scale invasion for more than four years.
Kiev has repeatedly warned of dwindling stocks of interceptor missiles for its Patriot air defence systems, which are used to defend against ballistic missile attacks.
Earlier, Russian missiles hit the southern port city of Odessa, killing at least two people and injuring four.
The military governor of the Odessa region, Oleh Kiper, reported the attack on Telegram on Saturday.
A missile hit an amusement park. There could be further victims under the rubble of fishermen's houses. Six cars were damaged, he said.
There was also another injured person in an unnamed place in the region, according to the post.
A residential building and two cars were also damaged.
The Russian Defence Ministry, in a statement, said there were strikes "on Ukrainian ports", adding that at least three cargo ships were attacked with drones in the ports of Pivdennyi and Odessa.
The ships were transporting goods for the Ukrainian armed forces, the ministry claimed. In Pivdennyi, fuel tanks were also targeted by attacks with "precision weapons," it said.
with dpa
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