According to Ukraine's State Emergency Services, the attack hit a housing block, killing 16 people.
Another four people, including a child, died when a missile hit a community center, while a third missile landed in a field. At least 38 people were injured, responders said.
We don't expect to find anyone alive, but there is a chance, said Yevhenii Yenin, the first deputy interior minister who spoke from the scene of the attacks.
Images from the scene showed the residential building torn apart and debris strewn across the ground.
For several weeks, fighting has raged across the Odesa region, which borders the strategically significant Black Sea. But some Ukrainian officials are cautiously optimistic that the regaining of Snake Island, a Ukrainian outpost on the Black Sea, could mean a reduction of shelling toward Odesa. It's now known why the enemy took Snake Island. State border service spokesman Andrii Demchenko said at a briefing Friday that they filled the territory with the means of destruction and fired from them. We hope the shelling of Ukraine will decrease. Russian officials in southern Ukraine have been attacked by pro-Russian officials in recent weeks, suggesting signs of growing resistance. Kremlin spokesman Dmitry Peskov denied on Friday that Russia targets civilian areas in Ukraine and repeated the frequent claim that it focuses its air strikes on buildings containing ammunition or training troops. He didn't provide any evidence that this was the case, as with previous claims after Russian attacks. Russia has made some slow but significant gains in the east of Ukraine since refocusing its invasion there. A Russian official in the Russian-backed Luhansk People's Republic said on Friday Russian troops had completely taken over an oil refinery in the embattled city of Lysychansk, eastern Ukraine, though Ukraine admitted only to partial Russian success. The Russian barrage on Lysychansk has been relentless, according to Serhii Hayday, head of the Luhansk region military administration. People dream of at least half an hour of silence, but the occupiers do not stop firing from all available weapons, Hayday said on Thursday.