A Briton and three Americans are among the hostages, Paul Weeditz, a spokesman for the American company, said.
A South African, an Italian and a Croatian were also taken along with a Nigerian oil worker, said Mr Weeditz, speaking from Houston. "There were no injuries we know of and no damage to the rig," he said.
A Texaco official in Nigeria, said the hostages were taken at gunpoint on Wednesday from the rig by a boatload of youths from the Ijaw ethnic group.
"They were taken to an undisclosed location and are being held until a ransom is paid," the official said.