Although the First Lady has not been in the limelight unlike her Tunisian and Egyptian counterparts, she wields considerable influence, the Al Arabiya channel reported.
She operates the airline with the approval of her husband even though it rivals the Libyan national carrier.
Her wealth was estimated at $30 billion by the France-based group International Coalition against War Criminals (ICAWC), which revealed the figure during the Lockerbie crisis in 1992. Her husband Muammar Gaddafi's wealth was estimated at $80 billion.
Safia Farkash al-Baraasi is the second wife of the Libyan leader. They came to know each other in 1971 when Gaddafi was admitted to a hospital where she worked as a nurse. They got married the same year and have six sons and one daughter, according to the broadcaster Sunday.
Libya has been rocked by anti-government protests since Feb 14 in which at least 6,000 people have died.