Fires burned out of control in parts of the capital overnight, sending black smoke billowing into the night sky, as firefighters struggled to control multiple blazes.
Thursday morning saw residents and emergency crews cleaning debris scattered around heavily damaged buildings in the city.
Four people, including the child, died in Kyiv, mayor Vitali Klitschko said on Thursday.
Nine people were killed in Odesa, and two in the southeastern city of Dnipro, where Russian attacks set residential buildings ablaze, according to regional officials.
President Volodymyr Zelenskiy said the night had proven that Russia did not deserve any easing of global policy or lifting of sanctions, with 100 people wounded alongside those killed.
"There can be no normalisation of Russia as it is today. Pressure on Russia must work. And it is important to fulfil every promise of assistance to Ukraine on time," he said.
Air force units shot down or neutralised 31 missiles and 636 drones, but 12 missiles and 20 drones hit in the 24 hours to 7am on Thursday, the air force said.
Deputy Prime Minister Oleksiy Kuleba said rescue operations were ongoing and the toll could rise, while Foreign Minister Andrii Sybiha urged the international community to act.
"All decisions required to increase pressure on the aggressor must be unblocked now," he said on X.
"It is immoral, counterproductive, and dangerous to delay sanctions against Russia or packages of support for Ukraine."
Klitschko said that Kyiv came under another attack early on Thursday, adding that a drone, flying very low, slammed into an 18-storey building.
Prosecutors put the number of injured in the city at 54.
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 missile debris had hit the sixth floor of an apartment building in the central Podil district.
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, Klitschko said.
Nine people were killed and 23 injured in an attack on a high-rise building in the southern city of Odesa, officials said.
"Last night, the city came under several waves of missile and drone attacks," Serhiy Lysak, the head of the local military administration, wrote on Telegram, reporting damage to infrastructure facilities and a residential building.
The regional governor said that port and critical infrastructure facilities in the city had also been damaged.
In Dnipro, regional governor Oleksandr Ganzha said that two people were killed and 30 injured in an evening and overnight attack on the city; he posted pictures showing residential buildings ablaze.
Another man was killed and four people injured in the surrounding region, Ganzha said.
In Kharkiv, Ukraine's second-largest city in the northeast, officials said two people had been injured in drone strikes.
