"As a result of the enemy attack, a 12-year-old child has been killed," Klitschko wrote on Telegram. "At the moment, 10 people are injured. That includes several medics."
Klitschko said rescue teams had rescued a mother and child from a building in a central district where the ground floor was badly damaged.
He also said a missile hit the sixth floor of an apartment building in the central Podil district.
Klitschko said a large fire had broken out in a building in a district in the north of the capital and four emergency medical workers were injured, while debris had fallen in several locations.
Russian attacks also triggered major fires in the southeastern city of Dnipro, injuring five people, regional governor Oleksandr Ganzha wrote on Telegram. Pictures posted online showed buildings ablaze.
In Kharkiv, Ukraine's second largest city in the northeast, officials said two people had been injured in drone strikes.
Russia attacked Ukraine overnight and throughout the day on Wednesday with hundreds of drones and missiles, targeting port infrastructure in the south, killing two people and wounding at least seven, Ukrainian officials said.
Russia launched 324 drones and three ballistic missiles overnight, starting at 6pm local time on Tuesday, Ukraine's air force said. Air defence units shot down or neutralised 309 drones, but the missiles and 13 drones hit nine locations, it said.
An air force report issued on Wednesday evening said Russian forces had later launched 361 drones and 21 missiles during a 13-hour period ending at 10pm. A total of 349 drones and 20 missiles were downed or intercepted.
Twelve drone strikes and one missile strike were recorded, as were 12 instances of falling debris.
"Just over the past 24 hours, there were brutal attacks on Dnipro, Cherkasy, Kharkiv, Kryvyi Rih, Chernihiv, the Donetsk region, and Zaporizhzhia," President Volodymyr Zelenskiy said in a post on X, adding that co-operation to strengthen Ukraine's air defences was a priority.
"We need air defence missiles every single day – every day the Russians continue their strikes on our cities."
On Tuesday, Ukraine and Germany agreed on defence co-operation plans and Kyiv also agreed on drone production in Norway.
Drones have assumed a prominent role in the four-year-old war pitting Kyiv against Moscow. Both sides have also devoted resources to developing ways to intercept drones and upgrade air defences.
"A new model of warfare is being introduced, drone-assault units that combine aerial and ground unmanned systems with infantry into a single integrated system," the Defence Ministry said in a brief statement on Telegram.
"This approach has already produced results in the south, where since February a large area of territory has been liberated, precisely thanks to the use of these advanced units."
