Daewoo has confirmed that nine of its employees, all South Koreans, had been captured.
There were 17 South Koreans at the facility. The attack comes less than a week after five Chinese telecoms workers were kidnapped in another part of the delta.
Separately, the rebel Movement for the Emancipation of the Niger Delta (Mend) is still holding captive three Italians and one Lebanese, employed by Italian oil company Agip, who were kidnapped on December 7.
The group, which is fighting for local control of oil assets and reparations for neglect and pollution in the delta, was responsible for a wave of attacks on the oil industry last February that cost more than 500,000 barrels a day in lost output.
Mend has said it was not involved in Wednesday's attack on the Daewoo base, but that it was probably a kidnapping and ransom demands should be expected.
Hostages in the Niger Delta are usually held in remote settlements before being released unharmed, after employers or local authorities pay money.
But last year a Nigerian and a Briton were killed in separate botched attempts by troops to free them.
The delta area accounts for all of Nigeria's oil production but residents say the region has been polluted and is neglected by the authorities.
It is estimated that a fifth of Nigerian output capacity has been shut down because of attacks.