The Brotherhood constituted cells to gather intelligence for launching attacks against the country's institutions, army personnel, judiciary, media persons, political and public figures, a statement read on state television said.
The group sought to send the information gathered to its international organisation abroad and some foreign bodies, security agencies claimed in the statement.
It employed hackers to gain access to government websites and some pages belonging to army and police officers "to gather and spread information to destabilize people's confidence in the country's institutions and delay completion of the road map," they said.
Morsi was removed by then-army chief Abdel Fattah al-Sisi nearly two years ago following mass protests against his rule. Last month a court sought the death penalty for the former president and 105 supporters of his Muslim Brotherhood in connection with a mass jail break in 2011.
Shater, the deputy of the Muslim Brotherhood supreme guide, has also been sentenced to death in a separate espionage case.