The Maran Centaurus was sailing from Kuwait to the Gulf of Mexico with a crew of 28 when it was seized early yesterday.
Nine armed pirates attacked the tanker and seized it, according to the coastguard.
The official said there were nine Greeks, two Ukrainians, one Romanian and 16 Filipinos on board the tanker.
Maran Tankers Management, the Greek managing company, said the ship was now heading towards the Somali coast.
A Greek navy frigate, taking part in the EU naval operation against piracy in the region, was shadowing the tanker, the Greek Defence Ministry said.
Heavily armed gangs from Somalia have made tens of millions of dollars in ransoms by seizing ships using the strategic shipping lanes that link Europe to Asia.
