AFP journalists in the capital heard several explosions before dawn, and air raid sirens sounded soon after that.
Ukraine's air force said it had downed all 10 missiles targeting the city and the health ministry said 53 people had been wounded, including two children.
Most injuries were caused by "glass shards, household items and the shock wave" as missile debris fell in eastern and southern parts of the city, the ministry added.
Russia's defence ministry said the armed forces had destroyed Ukrainian ammunition depots and drone construction sites, but did not elaborate.
The strikes came as Ukrainian President Volodymyr Zelensky arrived in Norway -- a key donor -- after a visit to Washington that failed to unblock a $60 billion aid package stuck in a divided Congress.
Ukraine "can't win without help," Zelensky told reporters following talks with Norwegian Prime Minister Jonas Gahr Store.
In a post on social media, he called Russia "a shameful country that fires rockets at night, hitting residential areas, kindergartens and energy facilities in winter".
- 'Enduring' support -
With the counter-offensive launched by Ukraine in June failing to yield the anticipated results, Zelensky is trying to rebuild support among Ukraine's allies amid growing fatigue.
Speaking alongside Zelensky at the White House on Tuesday, US President Joe Biden said the United States would "continue to supply Ukraine with critical weapons and equipment as long as we can.
"I will not walk away from Ukraine," Biden said, warning that a Ukrainian defeat would mean "would-be aggressors everywhere will be emboldened".
The Kyiv strikes came a day after a massive hacking attack on the country's top telecoms operator, which Ukrainian officials said might have been carried out by Russian security services.
Russian forces have also intensified attacks along the front line in southern and eastern Ukraine in recent days.
The conflict is expected to be a key topic for a European Union summit this week, where Ukraine is hoping for positive news on its bid for membership.
Speaking in the European Parliament on Wednesday, EU chief Ursula von der Leyen urged the bloc's 27 leaders to back massive financial aid for Ukraine, and Kyiv's ambitions for membership talks.
"We must give Ukraine what it needs to be strong today," the European Commission president told MEPs.
French President Emmanuel Macron also called for the EU to offer "full and enduring support" to Ukraine.
"Our collective security is at stake," he said.
German Chancellor Olaf Scholz said he would call for "sustainable, reliable financial support for Ukraine" at the summit.
- 'Ballistic' missiles -
Wednesday's strike was the second in a week, after another attack overnight Sunday to Monday in which eight missiles headed for the capital were shot down.
The strikes have come following a long period of relative calm for the capital.
Kyiv officials said an apartment building was damaged and had to be evacuated and the water supply in one city district was affected.
"The enemy used ballistic weapons," the Kyiv City Military Administration said.
"The enemy is intensifying the missile terror of Kyiv," it added.
There were also strikes Wednesday in the southern port of Odesa, where officials said nine Iranian-made Shahed drones had been downed.
Two employees of a car repair facility were injured by one of the downed drones and "a port infrastructure building was partially destroyed" by another, regional chief Oleg Kiper said.
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