Four speed boats carrying about 20 to 30 armed attackers arrived at the Bulford Dolphin facility off the country's southwestern coast at about 3am local time (0200GMT) on Friday.
Six Britsh men, one American and one Canadian were then abducted, according to a spokeswoman from Dolphin Drilling, a British-based subsidiary of Fred Olsen Energy, the Norwegian firm that owns the rig.
Sheena Wallace said: "We understand that the group [of kidnappers] has been in touch with the local companies about negotiations."
The Bulford Dolphin operates for the Nigerian oil company Peak Petroleum and Aberdeen, Scotland-based Dolphin Drilling operates the rig.
Haz Iwendi, a police spokesman, said in the Nigerian capital, Abuja: "No group has claimed responsibility and no demands have been made. Security agencies are trailing them to secure the release of the hostages as soon as possible."
Iwendi said the attack occurred near the Dodo River in the country's oil-rich southern delta. Kidnappings by activist militants or those seeking money have been common in the region in recent years.
Negotiations under way
Fred Olsen Energy said in a statement that it was negotiating with the hostage-takers.
"National and other authorities are co-operating in solving the situation ... . The drilling operation has been temporarily terminated. The incident has not caused any pollution nor damage to the rig," the statement read.
The kidnappings took place off
Nigeria's southwestern coast
Security sources said the rig sent a distress call during the attack and was picked up by a ship cruising nearby.
Non-essential staff have been evacuated to the city of Port Harcourt.
The Movement for the Emancipation of the Niger Delta (MEND) staged a series of attacks and kidnappings at oil facilities in January and February, but has typically acknowledged responsibility within minutes via email.
The timing of the attack is embarrassing for Nigerian authorities and particularly the navy, which was due to celebrate its 50th anniversary with an international fleet review by Olusegun Obasanjo, the president, in Lagos later on Friday.
Nigeria is Africa's largest oil producer and the world's sixth largest oil exporter with around 2.6 million barrels a day. It derives more than 95% of its foreign exchange earnings from oil.