Rescuers evacuated eight crew members, two of whom were injured. The search-and-rescue operation was ongoing.
Russian forces attacked the ship as it was leaving a Ukrainian port after being loaded with corn, the minister said. At the time of the attack, 18 people were on board: 17 citizens of Syria and India, along with a Ukrainian harbor pilot.
Ukraine's navy earlier reported that Russian forces fired three Kh-59/Kh-69 cruise missiles at the vessel, named Golden Leo, as it was leaving the combat zone carrying grain cargo. The ship is owned by a Turkish company. The strike hit the starboard side of the superstructure, sparking a fire on board.
The navy had earlier said five people were killed and the search for five others was continuing.
Ukraine's Air Force had previously reported five Russian missiles heading toward Odesa and Chornomorsk.