The early morning arrest of Mohammed Ali Bishr from his home in the Nile Delta was linked to a call for demonstrations at the end of the month, according to a security official.
The rallies have been called by a hard-line Islamist group called the Salafi Front, and not the Brotherhood.
Egypt has waged a sweeping crackdown on the Brotherhood since the military ouster in July 2013 of President Mohammed Morsi, a key member of the Islamist group, following mass demonstrations demanding his resignation.
In apparent retaliatory attacks, Egypt has seen a surge in bomb attacks. And while large suicide bombings usually target the police and the military, small-scale attacks with grenades and home-made explosive devices planted on trains, at universities and near police stations, are more frequent.
Today, a stun grenade on a train at Cairo's main Ramses train station set off panic and a stampede in which four people were hurt, another security official said. And outside the Helwan University in southern Cairo, a home-made bomb went off, wounding four policemen who were part of the force guarding the campus.