The crew of the sunken ship is still missing. The 18 people aboard the other ship have been rescued, rescue services told Bulgarian radio station BNR.
A search operation is underway about 150 kilometers east of the Bulgarian coastal town of Byala.
The sunken ship is said to have sailed under the Togolese flag and the other under the Palauan flag, according to the website maritime.bg.
The Bulgarian government is to hold an emergency meeting on Tuesday in response to the events.
The two merchant ships were in the exclusive economic zone of NATO member Bulgaria when they were attacked, according to unconfirmed reports in Bulgarian media.
On Monday, two people died aboard a ship that caught fire in the Black Sea outside Romania's exclusive economic zone. Ukrainian President Volodymyr Zelenskyy said Russian drones attacked the ship, which was reportedly loaded with grain.
