The attack, on a Shell field logistics base attached to the company's Nun river flow station, was carried out by youths from the Oporoma community in the delta's southern Bayelsa state, Shell said in a statement.
It said the station had been shut down as a result of the incident, resulting in a production loss of about 12,000 barrels a day.
Hafiz Ringim, the state's police commissioner, said a delegation had been sent to negotiate with the attackers, who were armed with assault rifles.
He did not say how many troops were taken hostage or how many attackers were involved.
However, a navy spokesman said the hostage situation had been caused by a "misunderstanding" between Shell and the local community over the implementation of an accord between the two sides.
Tensions have flared in recent months in the Niger Delta, home to Nigeria's multi-billion-dollar oil and gas industry, where most inhabitants live on an average of less than one dollar a day.
Separatist fighters and organised criminals have taken up arms against the government and the oil industry, abducting dozens of oil workers over the past nine months.
Their supporters argue that kidnappings and attacks are some of the only tools available to local people who want a share of the profits from the oil wealth beneath their lands.
Security concerns have recently forced Shell to close dozens of oil wells and rigs and evacuate workers from the volatile region.
More than two dozen foreign oil workers have been kidnapped this year.
Most hostage takings generally end peacefully, with the targets returned unharmed.