The Ukrainian air force said on the Telegram messaging app that its air defence systems destroyed eight Russia-launched ballistic missiles.
Reuters could not independently verify details of the weapons Russia deployed, although Reuters witnesses heard several explosions in Kyiv around that time.
Russia made no immediate comment on the attacks.
In nearly 22 months of war, Russia's numerous attacks on Ukraine have employed mostly Iranian-made Shahed attack drones or cruise missiles, which are propelled by jet engines and can be launched from ground, air or sea and fly at low altitude.
A ballistic missile, or rocket-propelled self-guided weapons system, arches upwards before descending towards its target, the US Centre for Arms Control and Non-Proliferation says.
Four people received medical aid in the Darnitskyi district in the southeastern part of Kyiv, the capital's mayor, Vitali Klitschko, said on Telegram.
A 21-year-old man received shrapnel injuries to his lower limbs, while three women suffered acute reactions to stress.
Emergency services sent to the southwestern district of Holosiivskyi quickly doused a fire sparked when part of a missile fell on the roof of a residential building, Klitschko added.
All the missiles launched were downed, Ukraine's air force said in a statement, while air defence systems destroyed all 18 Shahed drones in the southern region that Russia had launched overnight.
Meanwhile US President Joe Biden has invited Ukraine leader Volodymyr Zelenskiy to a December 12 meeting at the White House to discuss the ongoing war against Russia and the "vital importance" of continued US support of their defence efforts.
In a statement, the White House said the two would discuss Ukraine's "urgent needs"
The meeting comes as the White House looks to strike an agreement with Congress that would provide military aid for Ukraine and Israel.
Key topics during Zelenskiy's visit would include defence co-operation between the United States and Ukraine, "particularly through joint projects on the production of weapons and air defense systems, as well as the coordination of efforts between our countries in the coming year," Zelenskiy's office said.
- with AP
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