"I can confirm that Shettima Ali Monguno has been released today by his abductors," Borno State police chief Abdullahi Yuguda told AFP.
A security source who requested anonymity said the kidnappers were paid 50 million naira (USD 318,000, 242,766 euros), but the police chief declined to comment on the circumstances surrounding the release.
The ex-minister's son, Abubakar Ali Monguno, had told AFP that the kidnappers demanded a ransom hours after the Friday abduction outside a mosque in Maiduguri.
Criminal groups have also carried out attacks under the guise of Boko Haram.
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Monguno, 87, served as Nigeria's oil minister in the 1970s and held the rotating presidency of the Organisation of the Petroleum Exporting Countries (OPEC) in 1972.
He was among a group of elders who met President Goodluck Jonathan in Maiduguri in March to discuss the Boko Haram crisis.
He has repeatedly called for dialogue with the militant group and urged Jonathan to reduce the massive security deployment in the city and ease a curfew forcing all residents to stay indoors after sundown.