Fully loaded, the ship's cargo could be worth about $100 million. But the pirates would have no way of selling crude and no way to refine it in Somalia.
Instead, they were likely to demand a ransom, as they have in the past.
The Fifth Fleet later said the vessel was being taken to the pirate haven of Eyl in northern Somalia.
The Sirius Star is carrying 25 crew members from Croatia, Britain, the Philippines, Poland and Saudi Arabia, the statement said.
Christensen said the fate of the crew was unknown.
He said the latest hijacking occurred despite a 25 per cent drop in attacks by pirates since August.
The International Maritime Bureau has reported that at least 83 ships have been attacked off Somalia since January, of which 33 were hijacked.
Of those, 12 vessels and more than 200 crew were still in the hands of pirates.
Will Geddes, a security specialist in London, said most people's conventional idea of what pirates are is a fairly ramshackled bunch "but these guys have very sophisticated navigation systems and very good weapons which they are sourcing out of places like Mogadishu".
"They are very well resourced and some of the water craft they are using are very high-powered water craft. So they really do have in mind very specific targets and they plan their assault very, very carefully," he told Al Jazeera.
Admiral Michael Mullen, the chairman of the US joint chiefs of staff, said there were limits to what the world's navies could do once a ship has been captured because national governments often preferred to pay pirates ransom.
"I'm stunned by the range of it, less so than I am the size," he said, referring to the Sirius Star incident.
Oil prices rise
The tanker holds as much as two million barrels of oil - more than one quarter of Saudi Arabia's daily exports.
It had been heading for the US via the Cape of Good Hope at the southern tip of Africa, instead of heading through the Gulf of Aden and then the Suez Canal.
The hijacking helped lift global oil prices over $1 to more than $58 a barrel, although they later lost some gains.
Last week, the European Union started a security operation off the coast of Somalia, north of Kenya, to combat growing piracy and protect ships carrying aid agency deliveries.
It is the EU's first-ever naval mission.
Pirates are well organised in the area where Somalia's northeastern tip juts into the Indian Ocean.
They operate high-powered speedboats and are heavily armed, sometimes holding ships for weeks until they are released for large ransoms paid by governments or owners.
Somalia has had no effective government since the 1991 overthrow of Mohamed Siad Barre, the former president, touched off a bloody power struggle that has defied numerous attempts to restore stability.