A group of protesters have invaded three Shell oil stations in the Niger Delta, forcing the facilities to be shut down, the company said.
The demonstrators are accusing the oil giant of failing to fulfil an agreement to provide them with aid.
Shell refused to say how much oil had been cut off following the attack.
Militant groups have stepped up attacks on oil facilities in the region in recent months, demanding more local control of oil wealth for residents.
Shell said members of the Kula community living near the company's Ekulama 1, Ekulama 2 and Belema oil pumping stations had invaded the facilities.
Chevron also shut down its platform in the same area as a precaution.
A Chevron spokesman in Nigeria, Femi Odumabo, said government officials in charge of the area were holding negotiations with the protesters to address their problems.
Nigeria is Africa's biggest oil producer but militants have been demanding a greater share of the oil wealth for locals in the Niger Delta.
On Saturday seven oil workers - including four Britons - were freed after being held hostage in Nigeria.
The men were captured on 3 October when gunmen raided one of Exxon Mobil's residential compounds housing expatriate workers in the Niger Delta.
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