The MV Theresa VIII, a Singaporean-operated tanker, was taken on Monday in the south Somali Basin, 180 nautical miles north west of the Seychelles.
The vessel had been heading for the Kenyan port city of Mombasa, but was diverted north, the naval force said.
The EU naval force (Navfor) operates in the region to protect shipping.
Somali pirates, using "mother ships" to launch their small-boat attacks on vessels, have extended their range to an area off the Seychelles in recent months in order to evade the navies patrolling the Horn of Africa.
The MV Theresa VIII, the owner of which is based in the Virgin Islands, is a tanker of 22,294 deadweight tonnes, Navfor said.
It has emerged that guards aboard a Ukrainian cargo ship, the MV Lady Juliet, successfully fought off pirates in the Gulf of Aden on Monday.
Pirates firing Kalashnikov assault rifles and rocket-propelled grenades approached the vessel from their mother ship but came under return fire from a Navfor detachment protecting the ship.
Navfor supplies vulnerable ships with so-called vessel protection detachments, under certain circumstances.
Nobody was hurt aboard the Lady Juliet, which bears a St Vincent and The Grenadines flag, and any casualties among the pirates could not be confirmed.