Shettima Ali 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.
"The abductors got in touch and they put my father through on the phone, he spoke to us and said that he was fine. They made a ransom demand," the ex-minister's son, Abubakar Ali Monguno told AFP, declining to give a figure.
While no group claimed the attack, Boko Haram has targeted prominent figures around the northeastern city, with assassinations and kidnappings for ransom.
Some analysts have said that Boko Haram is increasingly relying on ransom payments as a means to finance their insurgency, which has left thousands dead since 2009.
Monguno was among the group of elders who met with 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, with a curfew forcing all residents to stay indoors after sundown.