In Kharkiv, 27 people were reportedly pulled out of the rubble.
In the Pechersk district, a fire broke out in a non-residential building.
Daryna Bodentchouk, a 17-year-old student interviewed by AFP near a damaged building in the capital, said she was upset. It's very scary, she said, explaining that a window had broken in her dormitory.
Three more people were injured by missile fragments in the Kiev region, said the head of the military administration, Ruslan Kravchenko.
In parallel with these nighttime attacks, a Russian strike killed a 70-year-old man in the southern city of Kherson, said Oleksandr Prokudin, the regional governor.
According to the Commander-in-Chief of the Ukrainian Army, Valery Zaluzhny, Russia targeted Ukraine with 41 missiles, of which 21 were shot down.
Ukraine is urgently demanding more anti-aircraft defense assets from its Western allies, and has set itself the goal of resuming its control of the skies above its territory.
It also increased its own missile and drone attacks on Russian territory this winter, aiming particularly the city of Belgorod.
The Duma, the lower house of the Russian Parliament, announced that it had voted on Tuesday a text appealing to the UN and parliaments around the world regarding Ukraine's criminal attacks against civilians on Russian territory. p>
Moscow also again denied having hit civilians in Tuesday's bombings, claiming, as always for two years, to only hit military objectives.
French diplomacy has accused Moscow of deliberately targeting civilian infrastructure.
The UN Human Rights Monitoring Mission in Ukraine (HRMMU) said it had noted the damage of these attacks on a school, a kindergarten and residential areas, such as in Kharkiv where a five-story building appears to have been directly hit by several missiles.
Hundreds of thousands of soldiers and civilians have been killed since the start of the x27;Russian invasion of Ukraine in February 2022.
However, there is no reliable assessment, neither side publishing detailed data and no independent organization, including the UN, is able to provide a comprehensive count of the dead and injured.