Lawyer Ahmed Soliman filed a lawsuit to ban the Sinai-based group's activities.
The US State Department has already designated the group a "foreign terrorist organization."
The group first emerged during the January 2011 uprising which toppled Hosni Mubarak.
Based in the northern Sinai Peninsula, near the Israeli border, its operations expanded dramatically after the ouster of Islamist president Mohamed Morsi.
Attacks that started in the peninsula are now taking place elsewhere in Egypt.
They have been targeting police and military personnel since Morsi`s ouster last July, in what they call revenge for a government crackdown on Islamists.
It has claimed responsibility for several bombings, including a suicide attack in February that killed two Korean tourists and their Egyptian bus driver.
They have also claimed responsibility for an attack on the police headquarters in the Nile Delta city of Mansoura last December.
NJF/NJF