Iranian state media and officials did not immediately comment on the claim by the Arab Struggle Movement for the Liberation of Ahwaz, which said it bombed the pipelines early yesterday morning in Khuzestan province.
The militants released online video they said showed one of the pipelines exploding. The Associated Press could not immediately verify the footage, though previous attacks have been attributed to the group.
The group said 2017 will be "very different to previous years since the movement has prepared detailed and precise plans to carry out a number of high-quality important operations against the Iranian enemy state."
Coordinated pipeline attacks could hinder Iran's efforts to recoup cash lost under international sanctions. The country has boosted production to around 3.8 million barrels of oil a day since the deal.
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Iran has faced low-level separatist unrest from Kurds in its northwest, the Baluch in its east and Arabs in its south since the 1979 Islamic Revolution. In recent months, however, such attacks have grown in scale.
Tensions also remain high between the Shiite power and Sunni-ruled Saudi Arabia.