The MENA news agency said Mohammed Morsi has been detained for 15 days for investigation into the charges. His detention can be extended as the inquiry continues. The news agency indicated that Morsi has already been interrogated.
The announcement comes after military strongman Gen. Abdel-Fatah el-Sissi called for mass demonstrations Friday to oppose what he called "terrorism," a clear reference to Morsi's Muslim Brotherhood. The Brotherhood's spiritual leader responded with a harsh denunciation of el-Sissi.
The Brotherhood also called for mass protests on Friday, escalating fears of clashes between the two opposing groups of demonstrators or with the military, which has pledged to keep order and prevent violence.
The case concerns the mass jailbreak of dozens of Muslim Brotherhood leaders during the popular uprising in 2011 that toppled Morsi's predecessor, President Hosni Mubarak. There have been many reports in Egyptian media that the Brotherhood collaborated with Hamas, its Palestinian wing, and Hezbollah militants in Lebanon to arrange the breakout.
Muslim Brotherhood officials have said they were aided by local residents in breaking out of prison, not foreigners.
In Gaza, Hamas spokesman Sami Abu Zuhri condemned Morsi's detention order. "The Egyptian decision is an attempt to drag Hamas into the Egyptian conflict," he said. "We call on the Arab League to bear its responsibility in facing the incitement against Hamas."
The Brotherhood has been demanding that Morsi, Egypt's first freely elected president, be restored to power. The military moved against him after several days of widespread demonstrations, when millions turned out to demand his resignation after just one year in office.
Egypt's military has been holding Morsi in an undisclosed location since deposing him on July 3. The MENA report did not indicate where Morsi is being held.
The MENA report said Morsi is being investigated over allegations of collaborating with Hamas "to carry out anti-state acts, attacking police stations, army officers and storming prisons, setting fire to one prison and enabling inmates to flee, including himself, as well as premeditated killing of officers , soldiers and prisoners."
Islamists on Thursday lashed out at the military, saying el-Sissi's call for mass demonstrations signals a plan to crush what they insist are their peaceful protests. The spiritual leader of the Brotherhood, Mohammed Badie, hiked up his rhetoric against el-Sissi, saying ousting Morsi was a worse crime than if the general had destroyed the Kaaba, Islam's holiest site - an attempt to fire up the religious fervor in the pro-Morsi camp ahead of Friday's rallies.
It was not clear what el-Sissi meant by seeking a mandate against violence - and how far the military would go. The most explosive move would be if troops were to eventually try to clear major Islamist sit-ins. The largest has been outside Cairo's Rabaa al-Adawiya mosque, where crowds some nights have grown to tens of thousands.
A more limited move would be for troops to take tougher action against any sign of Morsi supporters engaged in violence. Some Islamist protesters have been seen with weapons - though their opponents have been as well, and each accuses the other of sparking clashes. Another possibility is that the military would detain Brotherhood and other Islamist leaders who already face arrest warrants.
On Thursday, military spokesman Col. Ahmed Mohammed Ali said el-Sissi's call was "not a threat to any specific political group." He said the military respects peaceful protests.
But he said any violence or terrorism will be "dealt with decisively and with force" - signaling a likely tough approach on any sign of violence, which Islamists' opponents have largely blamed on the pro-Morsi camp.
He said a national reconciliation conference and a system of transitional justice, called for by military-backed interim President Adly Mansour, are the only way out of Egypt's current standoff.
The military dropped leaflets on Morsi supporters outside the Rabaah al-Adawiya Mosque, trying to reassure them about their safety.
"We are not against you so don't be against us. Don't raise your weapons in the face of your brothers, don't destroy, don't burn, and let us all be together against killing, violence and terrorism," the leaflets said.___
Associated Press writer Mohammed Daraghmeh in Gaza City, Gaza Strip contributed to this report.