It had a crew of 14, including eight Egyptians, four Indians and two Syrians, the coast guard said.
The ship reported a mechanical problem at 7 am Sunday, sent a distress signal and shortly after disappeared about 4 1/2 nautical miles (8 km) southwest of Lesbos, authorities said.
One Egyptian was rescued, a coast guard spokeswoman told The Associated Press.
She said that eight merchant ships, two helicopters and one Greek navy frigate were searching for survivors. Three coast guard vessels had difficulty reaching the area because of rough seas, she added. The spokeswoman spoke on condition of anonymity because the case was ongoing and she wasn’t authorised to speak to the media.
Northwesterly winds in excess of 80 kph (50 mph) per hour are blowing in the area, the national weather service said.