Ten people including a child were killed in an attack that hit a block of flats in the central city of Uman, officials said.
And a woman and her three-year-old daughter were killed in the city of Dnipro, according to the local mayor.
There were also explosions in the cities of Kremenchuk and Poltava, according to the Interfax news agency.
Ukrainian President Volodymyr Zelensky said 10 residential buildings were damaged in Uman, and an entire block in one of them was destroyed. He said the attacks showed further international action needed to be taken against Russia.
“Evil can be stopped by weapons – our defenders are doing it. And it can be stopped by sanctions – global sanctions must be enhanced,” he said in a tweet.
The head of the Kyiv city military administration said the capital had come under Russian missile attack for the first time in 51 days.
There were no immediate reports of civilian casualties in the capital.
Twenty-one out of 23 missiles and two attack drones were shot down by Ukraine’s air defence system, officials said in a post on the messaging service Telegram.
A video posted on Telegram by Ukraine’s State Border Service showed extensive damage to one apartment block in Uman.
The attacks come as Ukrainian forces are believed to be preparing for a military offensive with new equipment, including tanks, supplied by Western allies.
Russia has struggled to make headway in a winter offensive including a 10-month battle for control of the strategically important city of Bakhmut.
