Vitali Klitschko, the mayor of Ukraine's capital, said authorities found a body in one of the residential buildings struck there.
In other locations across Ukraine, authorities announced emergency blackouts after attacks on energy and other facilities knocked out power.
The barrage of strikes - including with missiles - came as air raid alerts were issued across Ukraine. At least 10 regions and cities reported that they were targeted.
The assault followed what have been days of euphoria after one of Ukraine's biggest military successes in the nearly nine-month Russian invasion - the retaking last week of the southern city of Kherson.
As its battlefield losses mount, Russia has in recent months increasingly resorted to targeting Ukraine’s power grid, seemingly hoping to turn the approach of winter into a weapon by leaving people in the cold and dark.
Among regions where officials reported strikes were Lviv, Zhytomyr, Khmelnytskyi and Rivne in the west, and Kharkiv, Ukraine’s second largest city, in the northeast.
Several missile strikes also hit Kryvyi Rih, President Volodymyr Zelenskyy’s native city, according to its mayor, Oleksandr Vilkul.
In Kyiv, a video published by a presidential aide showed a five-story - apparently residential - building on fire, with flames burning through apartments. The city mayor said three residential buildings were struck and that air defence units shot down other missiles. Vitali Klitschko added on his Telegram social media channel that medics and rescuers are being scrambled to the sites of the attacks.
Ukraine had seen a period of comparative calm since previous waves of drone and missile attacks several weeks ago.
The strikes came as authorities were already working furiously to get Kherson back on its feet and beginning to investigate alleged Russian abuses there and in its surrounds.
The southern city is without power and water and the head of the UN human rights office’s monitoring mission in Ukraine, Matilda Bogner, on Tuesday decried a “dire humanitarian situation” there.
Speaking from Kyiv, Ms Bogner said her teams are looking to travel to Kherson to try to verify allegations of nearly 80 cases of enforced disappearances and arbitrary detention it has turned up in the area and “understand whether the scale is in fact larger than what we have documented already”.
The head of the National Police of Ukraine, Igor Klymenko, said authorities are to start investigating reports from Kherson residents that Russian forces set up at least three alleged torture sites in now-liberated parts of the wider Kherson region and that “our people may have been detained and tortured there”.
“Mine clearance is currently underway. After that, I think, today, investigative actions will begin,” he said on Ukrainian TV.
The retaking of Kherson was one of Ukraine’s biggest successes in the nearly nine-month-old Russian invasion and dealt another stinging blow to the Kremlin. But large parts of eastern and southern Ukraine remain under Russian control and fighting continues.
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Mr Zelenskyy on Tuesday likened the recapture of the Kherson to the Allied landings in France on D-Day in World War II, saying both were watersheds on the road to eventual victory.
Speaking via video link to a Group of 20 summit in Indonesia, Mr Zelenskyy said Kherson’s liberation from eight months of Russian occupation was “reminiscent of many battles in the past, which became turning points in the wars”.
“It’s like, for example, D-Day — the landing of the Allies in Normandy. It was not yet a final point in the fight against evil, but it already determined the entire further course of events. This is exactly what we are feeling now,” he said.
The liberation of Kherson - the only provincial capital that Moscow had seized - has sparked days of celebration in Ukraine and allowed families to be reunited for the first time in months. But as winter approaches, the city’s remaining 80,000 residents are without heat, water or electricity, and short on food and medicine.
Still, US president Joe Biden called it a “significant victory” for Ukraine. Speaking on the sidelines of the G-20 summit, Biden added: “We’re going to continue to provide the capability for the Ukrainian people to defend themselves.”