Military council spokesman Gen. Shams Eddin Kabashi was quoted by the official SUNA news agency as saying that Abdullah and Abbas al-Bashir were taken into custody, without providing additional details or saying when it happened.
The arrests were part of a broad sweep against officials and supporters of the former government.
The Sudanese military ousted Omar al-Bashir last week, after four months of street protests against his 30-year rule marred by conflict, civil war and corruption. Al-Bashir is also wanted for genocide and crimes against humanity by the International Criminal Court for atrocities committee in the western region of Darfur.
"The arrests are ongoing of the ousted regime's figures in addition to those who are suspected of corruption," Kabashi said, adding that authorities are looking for a number of wanted fugitives. He said the detainees will be held in prisons in Khartoum and other cities.
The English-language Sudan Tribune said the brothers and al-Bashir's wife are suspected of having accumulated illegal wealth through the years of al-Bashir's rule.
The brothers' detention was likely another concession by the military to the protesters, who have demanded that all key figures and ranking officials from the former president's circle be arrested. A number of al-Bashir's close associates and former government officials have already been taken into custody since the military overthrew al-Bashir last Thursday. A number of them are also wanted by the International Criminal Court.
The military council that now runs the country said the former president was transferred Tuesday to Koper Prison in the capital, Khartoum, a facility notorious for holding political prisoners under al-Bashir.
Meanwhile, the Sudanese Professionals Association, which has been spearheading anti-government street protests since mid-December, released Wednesday together with several opposition groups a proposed blueprint for the transfer of power from the military to a civilian government.
Though the street protesters were overjoyed at al-Bashir's ouster, they were not happy with the military taking over and have demanded a swift handover of power to civilian rule. The military council has said it plans to rule for a maximum of two years as the country prepares for new elections.
The U.S. State Department said Thursday it supports a transition to a civilian government.
"The United States supports a transition to a peaceful and democratic Sudan led by civilians who represent the diversity of Sudanese society," spokesman Morgan Ortagus said in a statement. "The will of the Sudanese people is clear: it is time to move toward a transitional government that is inclusive and respectful of human rights and the rule of law. "
The protesters fear the army, dominated by al-Bashir appointees, will cling to power or select one of its own to succeed him. They have vowed to continue to protest, focusing on a sit-in outside the military headquarters in Khartoum, until the transfer of power is complete.
The two-page blueprint posted online envisages a civilian presidential council made up of "revolutionary figures" and a defense minister, the only representative from the military.
It also proposes the formation of a Cabinet of technocrats to run daily affairs of the state and a legislative council to draft laws and oversee the Cabinet until a new constitution is written.
"We have to continue our sit-ins until a transitional civilian authority takes over," the document says. "We have faith that our people's victory is coming and that no power can stop our people from achieving all their goals."
The military did not immediately comment on the document. The organizers of the protests called for a "one million people rally" to pressure the military to meet the demands of the protest movement. Chanting, dancing and clapping, protesters rallied in massive numbers in front of the military headquarters, the focal point of protests.
It's not clear what will happen next to al-Bashir, a pariah in any countries. The military has said it would not extradite him to the ICC but has not ruled out that a future civilian government could someday hand him over to the tribunal in The Hague, Netherlands.
Meanwhile, South Sudan's President Salva Kiir offered to mediate in Sudan's political crisis. In a letter seen by The Associated Press, Kiir this week pledged his support for a transition in which the rights of the Sudanese people are protected and offered to "mediate the on-going negotiations" among various groups.
Some in South Sudan are concerned that al-Bashir's departure will hurt their countries' fragile peace deal, which al-Bashir helped broker. South Sudan declared independence from Sudan in 2011, following decades of civil war.
But the new country subsequently sank into its own civil war, which ended with an agreement signed in September. The deal calls for opposition leader Riek Machar to return to South Sudan next month to once again become Kiir's deputy, though that looks increasingly unlikely as tensions continue.
One political analyst called Kiir's offer of mediation over al-Bashir a "hypocritical public relations" stunt.
"It doesn't make sense. You cannot leave your house in a mess and claim to clean your neighbor's house," Jacob Chol, professor at the University of Juba, told the AP.
ElHennawy reported from Cairo. Associated Press writer Sam Mednick in Juba, South Sudan, contributed to this report.
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