The country’s president called the attack “an open act of terrorism” against civilians in locations without military value.
Ukraine’s national police said three missiles hit an office building and damaged nearby residential buildings in Vinnytsia, which is located 268 kilometres (167 miles) south-west of the capital Kyiv.
The Ukrainian Emergency Service said 42 were missing after the air strike.
A Russian submarine in the Black Sea fired Kalibr cruise missiles at the city, and three children were among the dead, the deputy head of Ukraine’s presidential office, Kyrylo Tymoshenko, wrote on the Telegram messaging app.
Russia has not officially confirmed the strike, but Margarita Simonyan, head of the state-controlled Russian television network RT, said on her messaging app channel that military officials told her a building in Vinnytsia was targeted because it housed Ukrainian “Nazis”.
The missiles ignited a fire that expanded to engulf 50 cars in an adjacent car park.
The governor of the Vinnytsia region, Serhiy Borzov, said Ukrainian air defence systems shot down another four missiles over the area.
Ukrainian President Volodymyr Zelensky suggested the attack was deliberately aimed at civilians.
The strike happened as government officials from about 40 countries met in The Hague to discuss co-ordinating efforts to investigate and prosecute potential war crimes in Ukraine.
“Every day Russia is destroying the civilian population, killing Ukrainian children, directing missiles at civilian objects. Where there is no military (targets). What is it if not an open act of terrorism?” Mr Zelensky wrote on the Telegram messaging app.
Vinnytsia is one of Ukraine’s largest cities, with a population of 370,000.
Thousands of people from eastern Ukraine, where Russia has concentrated its offensive, have fled there since the start of the war.
Before the missiles hit Vinnytsia, the president’s office reported the deaths of five civilians and the wounding of another eight in Russian attacks over the past day.
One person was wounded when a missile damaged several buildings in the southern city of Mykolaiv early on Thursday, Ukrainian authorities said.
A missile attack on Wednesday killed at least five people in the city.
Russian forces also continued artillery and missile attacks in eastern Ukraine, primarily in Donetsk province after overtaking adjacent Luhansk.
The city of Lysychansk, the last major stronghold of Ukrainian resistance in Luhansk, fell to Russian forces at the beginning of the month.
Luhansk and Donetsk together make up the Donbas, a mostly Russian-speaking region of steel factories, mines and other industries.
Donetsk governor Pavlo Kyrylenko urged residents to evacuate as “quickly as possible”.
“We are urging civilians to leave the region, where electricity, water and gas are in short supply after the Russian shelling,” Mr Kyrylenko said in televised remarks.
“The fighting is intensifying, and people should stop risking their lives and leave the region.”
The British Ministry of Defence (MoD) said on Thursday that despite continued shelling in the Donbas region, Russian forces did not make major territorial gains in recent days.
The illegal and unprovoked invasion of Ukraine is continuing.
The map below is the latest Defence Intelligence update on the situation in Ukraine – 14 July 2022
Find out more about the UK government’s response: https://t.co/J6wyfBDtSt
?? #StandWithUkraine ?? pic.twitter.com/oqEsn6qxLO
— Ministry of Defence ?? (@DefenceHQ) July 14, 2022
“The ageing vehicles, weapons and Soviet-era tactics used by Russian forces do not lend themselves to quickly regaining or building momentum unless used in overwhelming mass – which Russia is currently unable to bring to bear,” the MoD said.
Both the Russian forces and Ukrainian militaries are seeking to replenish their depleted stocks of unmanned aerial vehicles to pinpoint enemy positions and guide artillery strikes.
Both sides are looking to procure jamming-resistant, advanced drones that could offer a decisive edge in battle.
Ukrainian officials say the demand for such technology is “immense” with crowdfunding efforts under way to raise the necessary cash for purchases.