According to the Russian governor of Rostov, the ships were fired on in Taganrog Bay, furthest into the Black Sea east of Crimea.
The attacks are the latest in a long series of Ukrainian attacks on ships carrying fuel to Russia.
During the night of Thursday, Ukraine also attacked a fuel depot in Tver, north of Moscow, reports the news agency NTB. In Stavropol, further south, Governor Vladimir Vladimirov said on Telegram that fuel tanks are on fire after a Ukrainian drone attack.
Ukraine attacks Russian oil facilities almost daily in an attempt to cut off the flow to the Kremlin's war chest. President Vladimir Putin has openly admitted that the country is suffering from fuel shortages and has banned the export of gasoline, diesel and jet fuel.
