Security agencies have already jailed five leaders of the Brotherhood and shut down its media outlets.
The prosecutor general's office said Badie, another deputy, Mahmoud Ezzat, senior member Mohammed El-Beltagy and popular preacher Safwat Hegazy are suspected of instigating the clashes with security forces outside a Republican Guard building near the mosque that killed 54 people most of them Morsi supporters in the worst bloodshed since he was ousted.
The Islamists have accused the troops of gunning down protesters, while the military blamed armed backers of Morsi for attempting to storm a military building.
The warrants highlight the armed forces' zero-tolerance policy toward the Brotherhood, which was banned under authoritarian leader Hosni Mubarak. The Brotherhood's refusal to work with the new interim leaders underscored the difficulties they face in trying to stabilize Egypt and bridge the deep fissures that have opened in the country during Morsi's year in office.
Morsi has not been seen since the July 3 coup, but Foreign Ministry spokesman Badr Abdel-Atti gave the first official word on him in days, saying he is in a safe place and is being treated in a "very dignified manner." No charges have been leveled against him, Abdel-Atti said.
Badie had appeared at the Rabaa al-Adawiya rally Friday, a day after an earlier arrest warrant against him was issued, also accusing him of inciting violence. On Wednesday night, he delivered a message to the crowd through a senior Brotherhood leader, an indication that he didn't want to make an appearance and endanger his security.
He spoke of Monday's violence, calling the troops that carried it out "traitors."
He urged supporters to stay camped out in the sit-in and mosques, using the holy month of Ramadan to pray for Morsi's deliverance. Badie also sought to dismiss accusations that his group used violence.
On Friday, Badie had delivered a fiery speech at the rally in person, telling those in the crowd that they will bring Morsi back to the palace on their shoulders. Following the speech, thousands of Islamists marched and clashed with Morsi opponents in the heart of Cairo and elsewhere in Egypt, leaving more than 30 dead and 200 injured.
In one of the most dramatic instances of violence that day, two Morsi opponents were killed when they were pushed off a roof by supporters of the ousted president in the city of Alexandria. Hamada Badr was stabbed and thrown off the roof, his father said. According to amateur video accessed by The Associated Press, a second man was hurled to his death. and Morsi supporters were seen beating his lifeless body. The video appeared consistent with AP's reporting from the area.
Since then, both sides appeared to be running a campaign of fear. The military and supportive media have depicted the Brotherhood and its backers as promoting violence. The Brotherhood and pro-Morsi protesters have portrayed Defense Minister Abdel-Fattah el-Sissi as head of a "militia" that is seeking to annihilate Islamists.