Air raid sirens sounded across the Mykolaiv region, which borders the vital port, before Saturday's early morning blasts.
"There are powerful explosions in the city! Stay in shelters!" Mykolaiv mayor Oleksandr Senkevich wrote on the Telegram messaging app.
Blasts had flattened part of an apartment building in the resort village of Serhiivka while residents slept on Friday, another in a series of what Ukraine says are Russian missile attacks aimed at civilians.
In his nightly video address on Friday, Ukrainian President Volodymyr Zelenskiy denounced the strikes as "conscious, deliberately targeted Russian terror and not some sort of error or a coincidental missile strike".
Kyiv says Moscow has intensified its long-range missile attacks, hitting civilian targets far from the frontline.
Russia says it has been aiming at military sites, with Kremlin spokesman Dmitry Peskov citing President Vladimir Putin's statements "that the Russian Armed Forces do not work with civilian targets".
A Russian missile earlier this week struck a crowded shopping mall in central Ukraine, killing at least 19 people.
Thousands of civilians have been killed since Russia invaded Ukraine on February 24 in what Moscow calls a "special operation" to root out nationalists.
Residents in Serhiivka helped workers pick through the rubble of the nine-storey apartment block, a section of which had been destroyed in Friday's early-morning strike.
"We came here to the site, assessed the situation together with emergency workers and locals, and together helped those who survived," Oleksandr Abramov, who lives nearby, said.
"And those who unfortunately died, we helped to carry them away."
Serhiy Bratchuk, spokesman for the Odessa regional administration, said 21 people had been confirmed killed, including a 12-year-old boy.
The strike on Serhiivka took place shortly after Russia pulled its troops off Snake Island, a strategically important outcrop about 140km southeast of Odessa that it seized on the war's first day.
The chief of Ukraine's General Staff, Valeriy Zaluzhny, accused Russia of failing to abide by its assertions that it had left Snake Island as a "gesture of goodwill".
On his Telegram channel, Zaluzhny said two Russian warplanes had taken off from a base in Crimea and bombed targets on the island on Friday evening.
He posted a video of what he said was the attack. Reuters could not confirm the authenticity of the video or the Russian action depicted.
There was no immediate Russian comment.
Russian forces had used Snake Island to control the northwestern Black Sea and impose a blockade on Ukraine, one of the world's biggest grain exporters.
Moscow denies it is to blame for an impending food crisis, which it says is caused by Western sanctions.
Putin met the president of Indonesia on Thursday and spoke by phone on Friday to the prime minister of India, promising both major food importers Russia would remain a big supplier of grain.
Russia's stepped-up campaign of missile attacks on Ukrainian cities coincides with its forces grinding out success on the battlefield in the east, with the aim of forcing Ukraine to cede Luhansk and Donetsk provinces.
Moscow has been on the verge of capturing Luhansk since taking the city of Sievierodonetsk last week after some of the heaviest fighting of the war.
Ukraine's last bastion in Luhansk is the small city of Lysychansk, which is close to being encircled.
"Private houses in attacked villages are burning down one by one," Luhansk Governor Serhiy Gaidai said on Telegram.
"With such a high density of shelling, we only have time to shelter the injured. Fires simultaneously in several places. We barely have time to eliminate large-scale fires in Lysychansk."
Pavlo Kyrylenko, governor of the Donetsk region, said four civilians were killed in the region in Russian shelling on Friday and 12 injured.
More weapons were needed in eastern and southern Ukraine, Zelenskiy said, as the Pentagon announced the US was sending two surface-to-air missile systems, four additional counter-artillery radars and ammunition as part of its latest arms package.
