The attack struck a civilian container ship flying the flag of Panama, according to the region's governor Oleg Kiper.
"Six people were killed... All the victims are citizens of Ukraine," Kiper said on Telegram.
He said in a later post the number of wounded had risen to 11 people.
"This is the third attack on a civilian vessel in the last four days," the governor added.
Russia has targeted Ukraine's coastal Odesa region throughout the war, hitting boats and grain silos in what Kyiv says is an illegal attempt to destroy its export capacity.
Ukraine was one of the largest exporters of grain in the world before Russia's invasion in February 2022, but repeated attacks on its port and storage facilities have severely curbed its output.
The attack comes two days after a Russian missile hit a Palau-flagged ship in the port of Odesa, killing one person aboard, according to local authorities.
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