BBC reporters heard loud blasts shortly after the air raid siren sounded.
Explosions rocked the central Shevchenkivskyi district as air defences shot down what were said to be Iranian-made Shahed drones.
Russia has repeatedly targeted Ukrainian energy infrastructure since October with missiles and drones.
And Kyiv Governor Oleksiy Kuleba accused Russia of “continuing its energy terror against our country” with the latest wave of drone attacks.
But the national energy grid manager Ukrenergo said that Wednesday’s strikes did not damage any energy facilities and hailed the “brilliant work of the air defence forces” in a post to its Telegram account.
President Volodymyr Zelensky said Ukrainian forces had shot down 13 Shahed drones, which he said amounted to all those launched by Russia on Wednesday.
Governor Kuleba said a drone fragment had hit an administrative office in the city and four residential buildings. But a spokesperson for the city emergency services told Ukrainian media that no victims had been reported in the strike.
One witness, named Svetlana, told the BBC that the first strike took place at 06:30 (04:30 GMT) local time.
“The rumble was like from a moped, such was the sound it made,” she said. “It fell behind the houses and then there was a strong roar, an explosion.”
She added: “Winter is coming, how can people survive? Lord, what do they want from us? They do not let Ukrainians live.”
Another Kyiv resident, Anton, told the BBC that falling glass shattered by the explosions had narrowly missed his sleeping children.
“Let this Putin die,” he said. “I didn’t do anything to him, but he does this to me.”
The strikes happened as UN humanitarian chief Martin Griffiths was in Kyiv, after visiting the southern cities of Mykolaiv and Kherson. He told the BBC they were a reminder of how Ukraine was “still suffering from the war right across the country, not just on the front lines”.
The urgent need was to help Ukraine restore energy supplies, including by providing generators to the country, as “electricity is the gateway to life”, Mr Griffiths added. “If you don’t have electricity, you don’t get warm, you don’t get hospital treatment, you don’t get to go to school, you don’t get to have transport.”
Ukraine has accused Iran of supplying Russia with “kamikaze” drones used in deadly attacks on 17 October, which Tehran initially denied.
Iran later admitted sending Moscow a limited number of drones “many months” before the war.
In response, Ukraine’s President Zelensky said this was a lie and that many more Iranian drones were being used.
Russia has been targeting the country’s energy grid in recent months in what Ukraine says is a bid to demoralise its population. Temperatures across Ukraine have dropped below freezing, but Martin Griffiths said there were no indications of a big new wave of Ukrainians fleeing their homes or their country.
Global leaders have said the strikes on civilian infrastructure amount to a war crime, but last week Russian President Vladimir Putin defended the attacks and said they were in response to a blast on the Russian bridge to annexed Crimea on 8 October.
The strikes come amid reports that the US is preparing to arm Ukraine with its state-of-the-art Patriot air defence system. Senior defence officials told the Reuters news agency that the announcement could come as soon as Thursday.
The system is among the most advanced in the world and is usually in short supply. Due to its long-range capability it could potentially shoot down Russian missiles and drones before they come within range of Ukrainian cities.
But unlike Ukraine’s existing air defence systems, Patriot systems require large crews to operate them, and it could take several months to train Kyiv’s forces to use it effectively.
Russia would likely view any attempt to arm Ukraine with Patriot defences as an escalation. Former president Dmitry Medvedev – who is now deputy chairman of the national security council – warned against the move last month.
Meanwhile, Ukraine says it has secured the release of 64 troops who were captured by Russia during fighting in the eastern Donbas region earlier this year.
President Zelensky’s head of office Andriy Yermak also said officials had secured the release of US citizen Suedi Murekezi.
Mr Murekezi was arrested by Russian troops while they occupied the southern city of Kherson in July, where he had been living for more than two years.
He was released from Russian custody in October, but prevented from leaving Donetsk province by Moscow’s officials as he did not have identity papers.