Supreme Guide Mohamed Badie, 70, was arrested Tuesday in Cairo's Nasr City during a crackdown by Egypt's army-backed government on the group and its followers, which includes ousted president Mohamed Morsi, Ahram Online reported.
The announcement Ezzat, 69, would be the temporary spiritual leader was posted on the website of the Brotherhood's Freedom and Justice Party.
Badie was the latest of the Brotherhood's senior leaders to be held by security forces. Six Brotherhood leaders have been charged with inciting the murder of protesters at the group's headquarters in the Cairo in June.
Morsi has been detained by the military since his ouster 3 July.
Tensions have been running high in Egypt since police stormed two protest camps by Morsi loyalists last week, leaving hundreds dead and thousands injured.
Also Tuesday, the Egyptian Army declared the Sinai Peninsula a closed military zone, one day after 25 off-duty policemen were killed, Israel Radio reported.
Egyptian army officials said they know who perpetrated Monday's attack and were cracking down on terror groups operating in the Sinai, the report said.
A senior Israeli official met with Egyptian security and senior interim government officials in Cairo to discuss security coordination, the radio report said.
Israeli intelligence estimates several thousand terrorists currently operate in the Sinai Peninsula and include fighters from Gaza, Saudi Arabia and Yemen, Haaretz said.
In Cairo, Hosni Mubarak's lawyer said Tuesday the ousted autocratic president could be released from custody in days, but state media said it could be two weeks. Farid el-Deeb told reporters the Cairo Criminal Court would likely release 85-year-old Mubarak this week after the court absolves him of charges he abused funds.
Mubarak and his two sons were charged with embezzling funds for presidential palaces. The sons, Alaa and Gamal, were ordered by the court to remain in custody.
Egyptian state media reported Mubarak would remain in custody for two more weeks under a previous judicial order before authorities decide whether to release him.
El-Deeb said in June 2011 Mubarak had stomach cancer "and the tumors are growing." He said a month later Mubarak had slipped into a coma.
The ousted leader, who remains in poor health, faces trial on several corruption charges and a retrial on charges of complicity in the killing of protesters whose revolt forced his ouster in February 2011.
Mubarak has said he knew nothing about any crimes committed.
He has been held for more than two years as some of those trials have proceeded.
Because his custody period exceeds the one allowable under Egyptian law, a judge could release him to await trial outside of custody, Justice Ministry officials and prosecutors told The Wall Street Journal.
The possibility of his release threatened to inject a volatile new factor into the standoff between Egypt's military and Islamist supporters of the deposed President Mohamed Morsi.
Mubarak's overthrow led to Morsi's popular election -- Egypt's first freely elected president. Mass protests led to Morsi's ouster at the hands of Egypt's military July 3. The military also backed Mubarak.
Morsi is accused of participating in the detention and torture of citizens, murder and attempted murder and disseminating false information, among other charges, the state Middle East News Agency said.
Members of his party who haven't been detained by the military say he is innocent and the charges against him are politically motivated.
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