"The number of dead as a result of a strike on a multi-storey apartment building has now risen to 10," Serhiy Bratchuk, spokesman for the Odesa regional administration said on his Telegram channel.
Earlier reports said six people had died in the night-time incident, including three children.
The missile came in the hours after Russian forces abandoned the strategic Black Sea outpost of Snake Island in what Ukraine is hailing as a victory.
Russia said it had decided to withdraw from the outcrop as a "gesture of goodwill" to show it was not obstructing United Nations efforts to open a humanitarian corridor allowing grains to be shipped from Ukraine.
Ukraine said it had driven the Russian forces out after an artillery and missile assault overnight.
"KABOOM!" tweeted Andriy Yermak, Ukrainian President Volodymyr Zelenskiy's chief of staff.
"No Russian troops on the Snake Island anymore. Our Armed Forces did a great job."
In another boost for Ukraine's struggle to beat back the Russian invasion, the United States said it would provide another $US800 million ($A1.2 billion) in weapons and military aid.
US President Joe Biden, speaking after a NATO summit in Madrid, said the members of the military alliance were united in standing up to Russian President Vladimir Putin.
"I don't know how it's going to end but it will not end with Russia defeating Ukraine," Biden told a news conference.
The retaking of Snake Island came after weeks in which momentum in the four-month-old conflict appeared to be shifting in favour of Russia, which has focused its firepower on capturing cities and towns in the Donbas region of eastern Ukraine.
The rocky outcrop of Snake Island overlooks sea lanes to Odesa, Ukraine's main Black Sea port, where Russia is blocking food cargos from one of the world's leading grain suppliers.
"The most significant aspect is that this could open the door to Ukrainian grain exports from Odesa, which is critical for Ukraine's economy and for the global food supply," Rob Lee of the US-based Foreign Policy Research Institute, said.
US Secretary of State Antony Blinken has accused Russia of deliberately causing world hunger as "blackmail".
Russia denies blocking the ports and blames food shortages on foreign sanctions it says limit its own exports.
"We do not prevent the export of Ukrainian grain. The Ukrainian military has mined the approaches to their ports; no one prevents them from clearing those mines and we guarantee the safety of shipping grain out of there," Putin said on Thursday.
Several military experts said that driving the Russians from Snake Island would not by itself be enough to unblock the ports.
"Does that mean that suddenly the grain flows? No it doesn't really," said Marcus Faulkner, a lecturer of War Studies at King's College London, noting that ports were still mined and that Russia could still intercept cargo ships at sea.
Mathieu Boulegue of the Chatham House think tank in London cautioned tat the Russian move could free up the assets deployed on Snake Island to strengthen its forces elsewhere on the Black Sea coast.
In the battle for Donbas, Ukrainian authorities said they were trying to allow remaining residents to leave the city of Lysychansk, where they believe about 15,000 people remain.
Russian forces have been trying to encircle Lysychansk since they captured Sievierodonetsk, on the opposite side of the Siverskyi Donets River, last week after weeks of heavy fighting.
Despite yielding ground and taking punishing losses in the Donbas in recent weeks, Ukraine hopes to inflict enough damage to exhaust Russia's advancing army.
6°C