The prosecutors will investigate whether the Brotherhood members had offensive weapons, took part in a public show of strength and possessed the group's leaflets and documents, the sources said.
A Brotherhood official said police initially arrested 180 people and released 40 of them on Friday.
Shatir, one of two deputies to Mohamed Mahdi Akef, the group's general guide, is the most senior member of the Islamist group detained since Mahmoud Ezzat, the secretary-general of its Guidance Office, was released in August last year.
An Interior Ministry statement said that the Brotherhood leadership had planned and incited acts of public disorder this week at al-Azhar University.
The Brotherhood is the country's largest opposition group, with 88 members in the 454-seat lower house of parliament. It says its aim is to persuade Egyptians by democratic means to choose an Islamic state.
Abdel Moneim Mahmoud, a Brotherhood official, said the sweep took in 180 students from the university's halls of residence, including Suhaib Gawdat el-Malt, whom he called the head of the free students union at the university.
Another prominent detainee is Ayman Abdel-Ghani, who runs the organisation's student section at the university, and three members of the teaching staff, he said.
The government refuses to recognise the Muslim Brotherhood and the police frequently harass its members by detaining them without charge, sometimes for months at a time.
But the Islamist group does maintain an office and is able to organise some events within limits.