The owner, state nuclear company Rosatom, says that the ship "Janina" was hit by at least two Ukrainian drones near the Russian port city of Novorossiysk.
"All 17 crew members have been rescued and are in good health," Rosatom said in a statement on Telegram.
Ukrainian President Volodymyr Zelenskyy confirmed on Telegram that the ship was attacked and that it sank.
Ukraine has previously attacked Russian-flagged ships in the Black Sea, which Ukraine says are used by Russia to transport oil and other sanctioned goods.
According to Zelenskyy, Ukraine also attacked three Russian oil refineries in the Russian republic of Bashkortostan overnight.
