The tanker reported several explosions and a fire at around 07:00 local time (05:00 GMT) while sailing from Tunisia to Romania. Romanian media quoted crews on nearby ships as saying the Wine Trader was hit by two drones.
A search and rescue operation involving two Black Hawk helicopters and two rescue boats has been deployed, but rough seas are hampering efforts. Four crew members are confirmed alive, and authorities are working to reach them while ensuring rescue team safety.
The incident is the latest in a spate of drone attacks along the west coast of the Black Sea. A swarm of Russian drones was detected overnight near Ukraine's Snake Island, not far from the scene. Moscow claimed two cargo ships carrying military cargo heading to Ukraine's Odesa port were hit during the crossing, though it did not name the vessels.
On Tuesday, two merchant ships were struck by drones further south off Bulgaria's coast, and one sank, leaving 11 crew members missing. Bulgaria said it suspected Russia was behind that attack and summoned the country's envoy.
The leaders of Romania and Bulgaria are due to discuss the escalating situation.