The pirates boarded MT Smyrni while it was sailing in the Arabian Sea on Thursday afternoon, a DGS statement issued late this evening said.
The DGS has asked the ship's manager and recruiting agent in Mumbai -- Dynacom Tankers Management -- to obtain information on the condition of the Indian crew.
The vessel, loaded with 135,000 tonnes of crude and owned by a Greek company, is headed towards the Somalian coast, it said.
The abducted Indians include the master of the vessel, which also had 14 Filipinos and a Romanian.
According to a BBC report from London, the hijacking is thought to have happened about 630 km off the Omani coast. This was only the second voyage for the tanker, which first set to sea in 2011.
Somali pirates often take over vessels in the busy shipping route in the Gulf of Aden, and have also come eastward up to the Arabian Sea in some cases.
The hijacking comes after a brief lull in pirate attacks. The lull is being attributed to the policy of having armed guards on vessels. According to the International Maritime Organisation, 17 ships and close to 300 crew are currently held by Somali pirates.