The Swede, who was the captain of the ship, was sailing south of the Peloponnese peninsula when the incident occurred.
“We were alerted by the chief officer who said that the captain had fallen overboard,” a merchant marine ministry spokeswoman told AFP.
“Two coastguard vessels are in the area and a number of private vessels are assisting the search. Weather conditions are good,” she said.
The Togo-flagged tanker Promise had sailed from the island of Salamis near Piraeus but its destination was unknown, the ministry said.
The ship, which was not carrying any cargo, was sailing around the south end of the island of Cythera, in the country’s south at the time of the man’s fall.
“He was onboard the tanker and had technical problems this morning, we are searching for him right now,” a police officer from Kythera told the Expressen newspaper on Sunday afternoon.
Neither the local police nor the merchant marine ministry could provide further information regarding the man’s fall.