Kyiv said the damage was done by debris after the missiles were shot down overnight.
More than 20 civilians have been taken to hospital for emergency treatment, including two children.
The Ukrainian army’s general staff said the projectiles had been identified as Iskander-M and S-400s, advanced missiles that are supposed to be fired at aerial targets targets.
Ukraine’s air force said it had shot down all 10 ballistic missiles and 10 drones that were launched on the capital.
Volodymyr Zelensky said Russia had “once again confirmed its title as a shameful country” with the attack and promised to retaliate.
Nearly 90 per cent of the soldiers who were serving in Russia’s army when it invaded Ukraine have been killed or injured, US intelligence believes.
A declassified report said Russia has suffered 315,000 casualties, representing 87 per cent of its initial invasion force.
Losses in personnel and armored vehicles have also “set back Russia’s military modernisation by 18 years,” a source told Reuters.
The Russian army began the war with 3,100 tanks, lost 2,200 of them and has had to “backfill” that force with T-62 tanks produced in the 1970s.
That has left it with only 1,300 tanks on the battlefield, the source quoted the report as saying.
“The scale of losses has forced Russia to take extraordinary measures to sustain its ability to fight,” it added.
