Amnesty said in a statement that Ahmed Hassan Bassyouni, 30, faced up to five years in prison for setting up a group on the social network concerned with doing military service and providing answers to questions about the military.
Egyptian officials could not be reached for comment on the case on Friday. Bassyouni appeared before the Al-Haram Military Court on November 24. The case has been postponed until November 29, Amnesty said.
"The Egyptian authorities must end the practice of trying civilians before military courts," Amnesty said. "This is an abuse of the Egyptian judicial system and the right to a fair trial. These trials are fundamentally unfair."
It added that Bassyouni, who was arrested on October 30, seemed to be under trial solely for publishing information readily available in the public domain.
Web activists said separately on Friday that two Egyptian opposition pages on Facebook had been deleted from the Internet ahead of Egypt's parliamentary election on Sunday.