They were arrested at an Al Jazeera Mubashr Misr office in Cairo's Agouza district on Thursday and ordered to be detained for four days pending investigations, the statement said. Authorities also seized "unlicensed" equipment, it added.
Prosecutors said they were informed that Al-Jazeera Mubashr Misr was "broadcasting news from three apartments in Agouza using unlicensed cameras, encryption, broadcast and telecommunication equipment."
Taher Saad and Hammam Mazen, are accused of possessing and operating wireless equipment and broadcasting audiovisual content without required licenses.
Al Jazeera's offices in Cairo have been closed since 3 July, when they were stormed by security forces hours after Morsi was toppled. The channel has transferred much of its broadcast equipment to Qatar.
The network has opened legal proceeding in international courts and before the United Nations over the alleged harassment of its staff and the jamming of its signals by the Egyptian authorities.
NJF/NJF