Reuters quoted an industry source as saying that armed men arrived at the facility yesterday morning in several boats, opening fire on security and abducting the five expatriates.
The newswire reported that those kidnapped were one Australian, two New Zealanders, one Venezuelan and one Lebanese.
The incident came as the rebel Movement for the Emancipation of the Niger Delta (MEND), which has been responsible for most of the attacks on the Nigerian oil industry, called off a one-month truce.
But a MEND spokesman reportedly told Reuters that the group was not involved in the raid on the Royal Dutch Shell rig in Soku.
Bombings, kidnappings, armed robberies and other attacks have risen in the Bayelsa, Delta and River states, slashing about 30% of the country's oil output in May.
The rising levels of violence and insecurity prompted the British Government last month to advise all of its nationals to leave the three core states of Nigeria's southern Niger Delta, Africa's premier oil-producing region.