Earlier on Tuesday, a court upheld an order from the prosecutor’s office freezing the assets of 25 leading members of the Brotherhood and allied Islamist parties.
Mr El Haddad, however, was detained with two other Brotherhood officials in an apartment in Cairo. He served as chief of staff to deputy Brotherhood leader Khairat El Shater and is the son of Essam El Haddad, an aide to deposed Islamist president Mohamemd Morsi.
Mr El Haddad, the Brotherhood’s main point of contact with international media before the military started arresting the group’s members, is charged with inciting the killing of protesters.
Many of the Brotherhood’s top leaders have been detained on similar charges since the army deposed Mursi on July 3, triggering the worst violence in Egypt’s modern history.
At least a thousand people have been killed since then, comprising mostly supporters of the deposed leader but also scores of members of the security forces.
Mr Morsi, who is being held at an undisclosed location, has himself been charged with inciting killing and violence. Besides Mr Morsi, the Brotherhood’s three top leaders are also in jail, together with the head of its political party. It is the toughest crackdown on the Islamist group in decades.
Mr El Haddad was arrested together with Hossam Abu Bakr, a provincial governor under Mursi, and Mahmoud Abu Zeid, a member of the group’s executive board.
Gunmen also killed an Egyptian military officer and wounded three soldiers in an attack on an army vehicle northeast of Cairo on Tuesday, security sources said, raising concerns that an Islamist insurgency is spreading beyond the Sinai.
The number of militant attacks has risen since the army toppled Mr Morsi. Most of the attacks on the army have been limited to the relatively lawless Sinai. Tuesday’s attack took place in Sharkia province in the Nile Delta.