Ten buildings were damaged in the attack on Kryvyi Rih, Ukrainian officials said, one of several Russian missile strikes overnight.
Three of the people who were pulled out of the rubble were in serious condition, according to Ihor Klymenko, Ukraine’s minister of internal affairs.
Photos posted by Mr Klymenko on Telegram showed a building on fire and emergency services evacuating the injured.
Three people were also killed on Friday after a Russian bomb struck the village of Odradokamianka in the Kherson region of southern Ukraine, Mr Klymenko said, while three people were also injured in a Russian missile attack in the eastern city of Sumy.
Separately, Russian forces also struck the Odesa region in the west with drones for the fifth time in a week, regional governor Oleh Kiper said. No casualties were reported.
It comes as Moscow continues to try to strengthen its position politically with local elections in areas it has illegally annexed, including some it still does not control.
The elections are not internationally recognised and are widely considered to sham votes.
Also on Friday, a funeral was being held for an 18-year-old who was among 16 people killed on Wednesday in a Russian attack on a market in Kostiantynivka in Ukraine’s eastern Donetsk region.
The attack, which wounded 33 others, destroyed the market and overshadowed a two-day visit by US secretary of state Antony Blinken.
Mr Blinken’s visit aimed to assess Ukraine’s three-month-old counter-offensive, with the US government announcing a further one billion dollars (£801 million) in aid.
Meanwhile, the UK has announced it will host a global food security summit in November in response to Russia’s withdrawal of a Black Sea grain deal and attacks on Ukraine’s grain supply.
Rishi Sunak has said he will use his visit to the G20 summit to “put pressure" on Moscow, amid global concerns over the blockade of grain out of Ukraine.
“One of the priorities I have being here is to highlight the impact of Russia’s war on millions of vulnerable people around the world. And that’s the impact of food prices,” Mr Sunak said.