Mr Badie is accused of inciting the violence in Cairo on Monday in which at least 51 people were killed.
Many Brotherhood members are already in detention and warrants are said to have been been issued for hundreds more.
Meanwhile, a foreign ministry spokesman has said on Wednesday that ousted President Mohammed Morsi is being held in a “safe place”.
Badr Abdul Atti told reporters he did not know where the 61 year old was, but that he was being treated in a “very dignified manner”.
“For his own safety and for the safety of the country, it is better to keep him in a safe place. Otherwise, the consequences will be dire,” he added.
Mr Abdul Atti is reported to have denied that Mr Morsi was being detained at the Presidential Guard barracks in Cairo, as many believe.
The Brotherhood, to which he belongs, says his ousting by the military a week ago amounted to a coup.
Its supporters have since been staging protests outside the capital’s Rabaa al-Adawiya mosque, not far from the barracks, demanding his release and reinstatement.
The movement’s political wing, the Freedom and Justice Party (FJP), has said it will not accept an offer to join the cabinet being set up by interim Prime Minister Hazem al-Beblawi, a 76-year-old economist and former finance minister who was appointed on Tuesday.
Prosecutors also said last Wednesday they had ordered 200 people – believed to be Brotherhood members – to be held in custody for at least 15 days pending further investigation into accusations of murder, incitement to violence, carrying unlicensed weapons and disrupting public order. Another 450 have been released on bail.
Badie had appeared at a rally outside the mosque last Friday , telling the crowd: “We shall stay in the squares until we bring President Morsi back to power.”
Meanwhile , Saudi Arabia, the United Arab Emirates and Kuwait – who are opponents of the Muslim Brotherhood – have promised Egypt’s interim government $12bn (£8bn) in grants, loans, and gas and oil.
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