Five South Koreans and one Nigerian were taken from the site near Port Harcourt on Wednesday.
A coalition of Nigerian militant groups has claimed responsibility for the kidnappings and said they killed at least five Nigerian troops during the attack.
The Joint Revolutionary Council, which said it is made up of members of the Movement for the Emancipation of the Niger Delta and two splinter groups from another movement, demanded the release of two jailed ethnic Ijaw leaders.
The attackers, armed with rocket launchers, approached the oil rig near Port Harcourt by boat and overpowered members of the Nigerian navy who were guarding at the site. Six Daewoo boats were reportedly destroyed in the attack.
Three of the kidnapped South Koreans are from Daewoo Engineering and Construction, and the other two are from the state-invested Korea Gas Corporation, said South Korea’s foreign ministry.
Nine other Koreans working on the oil field managed to escape the kidnappers.
On Friday, a group of unidentified militants who were demanding jobs and money kidnapped eight foreign oil workers from an oil platform off Nigeria's southeastern coast. They were released on Sunday.
Unrest has been common in the oil-rich southern delta region of Nigeria for years, and in recent months armed militants have stepped up a campaign against the oil industry, blowing up oil pipelines and kidnapping foreign workers.
The kidnappings follow a visit to South Korea by Edmund Daukoru, Nigeria's oil minister, to promote investment in Nigeria's oil sector.
Daukoru, who is also president of the Organisation of Oil Exporting Countries (OPEC), said at a news conference in South Korea that Nigeria takes seriously a spate of kidnappings of foreign oil workers in the country.
"We condemn any form of hostage-taking as officials and we'll do everything possible to stop it," he said.