The Mattariya prosecution in Greater Cairo ordered on Tuesday the 15-day detention of a man pending investigation into his alleged creation of a Facebook page titled "Mattariya against the Coup" inciting to violence against members of the police.
The prosecution has also accused the defendant of joining a terrorist group and attempting to topple the regime. Arrest warrants have been issued for three other people.
In January, the Ministry of Interior said it had begun arresting Internet users who utilised social media websites to incite violence against the police or against citizens.
The announcement was followed by the arrest of dozens of alleged Muslim Brotherhood members accused of administrating Facebook sites that advocated terrorism against the state.
The 3 July 2013 ouster of Egypt’s first freely-elected president Mohamed Morsi, which ended nationwide mass protests against him and the Islamist Brotherhood group from which he hails, was described by Brotherhood members and loyalists as a "coup d'etat" that sabotaged democracy.
Hundreds of Brotherhood members and sympathisers were killed during the forced dispersal of protest camps held in Cairo and Giza last August calling for Morsi’s reinstatement, and thousands were arrested. The state has since maintained an intensive security crackdown on all Brotherhood supporters, with most of its leaders now behind bars.
In December, the Brotherhood was pronounced a terrorist organisation by the Egyptian government who accused it of orchestrating attacks against the police and the army -- a designation upheld by a court in February.
Terrorist attacks against the army and police have killed hundreds of personnel since Morsi's ouster. The Brotherhood denies any links to the violence.