Shell declared a force majeure on Tuesday - a legal clause allowing producers to miss contracted deliveries because of circumstances beyond their control - for the remainder of July, August and September.
It did not indicate the quantity of crude involved, but observers believe given that Bonny is one of Shell's two main terminals in Nigeria, it is likely to involve significant volumes.
Axel Busch, an oil expert from the Petroleum Intelligence Weekly, told Al Jazeera that he thought the reduction was about 130,000 barrels a day.
The announcement had an immediate effect on the oil price. Brent North Sea crude for September delivery gained 18 cents, rising to $126.02 a barrel.
New York's main contract, light sweet crude for September, climbed 32 cents to $125.05 a barrel.
John Terret, Al Jazeera's business analyst, said that there are a "myriad of reasons" for the global increase in oil prices, but unrest in key oil-producing regions is a major one.
"The supply and demand model is so tight at the moment that when any one of these regions experiences a problem, there is a spike in oil prices.
"Now, the price is at its lowest since May. That is partly because Shell in Nigeria confirmed it would not be pulling out of the country, but would instead not be able to meet some contracts due to the damage to its pipelines."
Precious Okolobo, a Shell spokesperson, confirmed damage to the Kula pipeline on Monday, but was unable to confirm claims made by Mend of an attack on a second pipeline.
Monday's attack is the fourth time Shell has resorted to a force majeure this year.
Most recently, in June, it was forced to cut production at its offshore Bonga oilfield, following an attack by the movement, made up of disparate groups of fighters. It resumed full production only on July 9.
The attack on the Bongo terminal, 120km off the Nigerian coast, caused heightened concern over the movement's ability to strike the oil industry.
Several foreign firms, including French tyre company Michelin and oil-servicing firm Wilbros, have left the Niger Delta because of security problems.
The unrest has reduced Nigeria's oil output by a quarter, causing it to lose its position as Africa's biggest oil producer to Angola, according to figures from the Organisation of Petroleum Exporting Countries (Opec).