President Volodymyr Zelensky blamed Russia for the strike, saying more people were trapped beneath the wreckage.
Russian air strikes over Ukraine have ratcheted up in recent weeks, as have incursions in the opposite direction.
Kyiv has for months said it is preparing for a major offensive against Moscow's occupation forces, as it looks to reclaim territory lost since Russia invaded in February 2022.
Saturday's strike affected two residential buildings, the president said.
"The Russians attacked the city," Zelensky posted on Facebook on Saturday.
"They hit between two two-story residential buildings. Unfortunately, there are people under the rubble."
Video posted by Zelensky showed rescue workers searching the destroyed building, to the sound of industrial drills.
"Five children were wounded by the enemy in Pidhorodnenska community," said Serhiy Lysak, governor of Dnipropetrovsk region.
"The condition of the three boys is now assessed by doctors as serious. They are in operating rooms."
"The total number of injured increased to 20. Of these, 17 are hospitalised," he added.
"Under the rubble of a mangled house, rescuers continue to search for people. There is probably a child there."
Also on Saturday, Ukrainian shelling killed two people in Russia's Belgorod, a border region that has been hit by repeated attacks this week, the local governor said.
Belgorod border villages have been hit by unprecedented shelling, and the latest deaths bring the overall toll to seven this week.
bur-leg/mca
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