A senior military officer told AFP on Thursday the army was "preventively" holding Morsi, whose government unravelled after the military gave him a 48 hour ultimatum in the wake of massive demonstrations against him on 30 June, exactly a year into his rule.
Warrants have been issued for the arrest of a total of 300 Brotherhood officials, state media reported.
Morsi "is being held preventively for final preparations," the military official said, suggesting the Islamist might face formal charges over accusations made by his opponents.
Morsi had been summoned for questioning by a court over his escape, along with other inmates, from prison during the revolt that overthrew his predecessor Hosni Mubarak in 2011.
The military official suggested he may now be charged by prosecutors in the case.
Morsi was detained along with senior aides after issuing a defiant call for supporters to protect his elected "legitimacy," in a recorded speech hours after the military announced his ouster.
Gehad El-Haddad, senior official of the Muslim Brotherhood's Freedom and Justice Party (FJP), reported that Morsi was seperated from his presidential team and transported to the headquarters of the Ministry of Defense alone.
"We had to confront it at some point, this threatening rhetoric," the military officer said.
"He succeeded in creating enmity between Egyptians," he added.
Police have begun arresting leaders of Morsi's Muslim Brotherhood movement, an interior ministry general told AFP. Saad El-Katatni, head of Morsi's Freedom and Justice Party, was already in custody, he added.
Thousands of Morsi's supporters remained camped out in northern Cairo, but Egyptian television stations stopped broadcasting live feeds of the pro-Morsi rally after the military announced his overthrow.