He is to be questioned for an initial 15-day period, a judicial order said.
Since Mr Morsi, the country's first democratically elected president, was ousted, dozens of people have died in clashes between his supporters and opponents. Militants have also staged deadly attacks in the Sinai peninsula.
The army chief, Gen Abdel Fattah al-Sisi, has called on people to take to the streets to give the military a mandate to confront violence and "terrorism".
The judicial order says the former president is suspected of conspiring with Hamas, which rules the Gaza Strip and has strong links with Mr Morsi's Muslim Brotherhood, during the uprising against former President Hosni Mubarak.
He is accused of colluding with the Palestinian group to storm police stations and jails, "setting fire to one prison and enabling inmates to flee, including himself, as well as premeditated killing of officers, soldiers and prisoners".
Mr Morsi and several Muslim Brotherhood leaders were freed during a breakout at a Cairo prison in January 2011.
The BBC's Jim Muir in the Egyptian capital says the order provides legal cover for the continued detention at a time when the UN and Western powers are calling for the ousted president to be released or properly charged.
A spokesman for the Muslim Brotherhood, Gehad el-Haddad, described the accusations as "ridiculous". He told Reuters news agency that the order marked the return of the "old regime".
Hamas itself said there was not a shred of evidence of its involvement in the prison break.
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