The attack began hitting different districts of Kyiv in the early hours of Saturday, with more waves coming as the sun came up.
The air raid warning lasted a total of six hours.
President Volodymyr Zelenskiy said more than 70 Iranian-designed Shahed kamikaze drones had been launched at Ukraine, and that most - but not all - had been downed.
Volodymyr Zelenskiy says Russia launched more than 70 drones at Ukraine, most of which were downed. (AP PHOTO)
The air force subsequently announced it downed 71 Shahed drones and one missile.
Mayor Vitali Klitschko, writing on the Telegram app, said the attack had injured five people, including an 11-year-old girl, and damaged buildings in districts all across the city.
Fragments from a downed drone had started a fire in a children's nursery, he said.
Zelenskiy pointed out that the attack had come in the early hours of the day when Ukrainians commemorate their worst national tragedy - the 1932-33 Holodomor famine in which several million people starved to death.
"Wilful terror ... The Russian leadership is proud of the fact that it can kill," he wrote on Telegram.
Ukraine's leadership has previously drawn parallels between Holodomor and Russia's current invasion.
Ukraine and more than 30 other countries recognise Holodomor as a genocide of the Ukrainian people by the Soviet Union, which ruled Ukraine at the time and sought to crush its desire for independence.
Moscow denies the deaths were caused by a deliberate genocidal policy and says that Russians and other ethnic groups also suffered because of famine.
Russia has attacked Ukraine with more than 70 Iranian-designed Shahed kamikaze drones. (AP PHOTO)
The target of Saturday's attack was not immediately clear, but Ukraine has warned in recent weeks that Russia will once again wage an aerial campaign to destroy Ukraine's energy system, as it sought to do last winter.
Ukraine's energy ministry said almost 200 buildings in the capital, including 77 residential ones, had been left without power as a result of the attack.
"It looks like tonight we heard the overture - the prelude to the winter season," Serhiy Fursa, a prominent Ukrainian economist, wrote on Facebook.
The attack came after Russian officials said on Friday Ukraine had launched one of its largest drone attacks on the Crimean peninsula since the Russian invasion.
They did not mention any casualties or damage.
The governor for the Russian-occupied part of southern Ukraine's Kherson region, Vladimir Saldo, said Ukraine launched a major drone attack on Crimea early on Friday.
He said dozens of drones were shot down over the province and the northern part of Crimea.
Russian authorities said air defences downed 13 Ukrainian drones over Crimea and three more over southern Russia's Volgograd region.
Deputy Prime Minister Olha Stefanishyna says Ukraine's determination "has remained the same". (EPA PHOTO)
Ukrainian officials did not comment on the Russian reports.
Speaking during a visit to Germany, Deputy Prime Minister Olha Stefanishyna said European countries were displaying increased war-weariness but nothing had changed in Ukraine's will to combat Russian aggression.
"Our determination has remained the same," she said.
Stefanishyna holds responsibility in Zelenskiy's government for European and Euro-Atlantic integration.
Stefanishyna said she was reading headlines about war-weariness, and had heard while travelling through European Union member states that the war was dragging on for too long.
"We should not count the days; we should see how things develop," she said after more than 600 days since the Russian invasion.
with DPA, AP
