The strikes hit the small town of Serhiivka, about 30 miles (50km) southwest of the Ukrainian port city, before dawn on Friday.
So far 41 people have been rescued.
Moscow insists it only hits military infrastructure, but thousands of civilians have been killed since the war began in February.
A Ukrainian army general says Russia is often using inaccurate Soviet missiles, and this is causing significant loss of civilian life.
Putin ‘may now become more dangerous’ – live updates on Ukraine war
Another 30 people were injured in the assault, according to Odesa officials.
A multistorey apartment building and two holiday camps were hit, local reports claimed.
Sixteen of those killed were in the block of flats, and a total of 152 people lived there.
• Ukrainian forces are desperately hanging on in the city of Lysychansk
• The US has pledged to provide an additional $800m (£660m) in weapons and military aid
• Meanwhile, the UK is going to spend 2.5% of GDP on defence by the end of the decade, Johnson says
• 202 missiles were fired on Ukraine in the second half of June, a Ukrainian army general says, compared with 120 missiles in the first half of the month
• The EU flag has been installed in Ukraine’s parliament after the country became a candidate to join the trading bloc
Russia’s ‘gesture of goodwill’ questioned
The strikes come after Russia claimed it was withdrawing from Snake Island as a “gesture of goodwill” to show it was not obstructing attempts to establish a humanitarian corridor that would allow grain to be shipped from Ukraine.
Snake Island, an outcrop in the Black Sea, become a symbol of Ukrainian resistance in the early days of the war when a soldier was recorded telling a Russian warship to “go f*** yourself”, but has since been occupied by Kremlin forces.
Officials in Kyiv offered a different explanation, saying they had managed to drive Russian forces away from the island after an artillery and missile assault.
The UK Ministry of Defence reached a similar conclusion, saying: “The Ukrainian armed forces conducted attacks against the Russian garrison in the past few weeks using missile and drone strikes.
“In addition, it used anti-ship missiles to interdict Russian naval vessels attempting re-supply the island.
“Russia has highly likely withdrawn from Snake Island owing to the isolation of the garrison and its increasing vulnerability to Ukrainian strikes, rather than as a ‘gesture of goodwill’, as it has claimed.”
President Volodymyr Zelenskyy has hailed Russia’s pullback from Snake Island as a strategic win.
In his nightly video address, he said: “It does not yet guarantee security. It does not yet ensure that the enemy will not come back.
“But this significantly limits the actions of the occupiers. Step by step, we will push them back from our sea, our land and our sky.”
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