Ukrainian naval drones attacked the 'Engineer Smirnov' tugboat and 'Section-179' barge in Russia's Taganrog Bay on the evening of June 8, Russian Telegram channel Baza said.
Russian media traditionally accuses Ukraine's Defense Forces of carrying out the attack.
Two crew members suffered minor injuries.
The barge sustained minor damage above the waterline, and the tugboat had its windows shattered, the tugboat's captain claimed.
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The tugboat's operational capabilities were not compromised, prompting the captain's decision to return to the port of Azov in Russia's Rostov Oblast, Baza wrote.
Located in the bay's northeast, Taganrog Bay is the Azov Sea's largest bay.