The Mada Masr website said Bahgat, 37, was ordered detained for four days for questioning on suspicion of "spreading false news aimed at harming national interests."
Bahgat was detained overnight after he responded to a military summons over his investigative reporting on a military trial that the army has not officially confirmed or denied.
The New York-based Committee to Protect Journalists called on Egypt to release Bahgat, who was a prominent human rights defender before entering journalism.
Human Rights Watch describes Bahgat, founder of the Egyptian Initiative for Personal Rights, as "a leading defender of civil rights and liberties in Egypt" who played a prominent role in the 2011 revolution that toppled longtime president Hosni Mubarak.
