Bishoy Kamel, a Coptic-Christian teacher from the Upper Egyptian Governorate of Sohag, was arrested on Monday.
Mohammed Safwat, an Egyptian, pressed against Kamel, who has been detained for four days pending investigation.
Kamel has admitted managing the page of the popular social networking site but claimed it was attacked by hackers on Saturday, al-Ahram Online said.
Islamist lawyers lodged a complaint with Egypt's attorney-general last June against a Coptic business tycoon, Naguib Sawiris, who posted a cartoon of Disney characters Mickey and Minnie Mouse dressed in Islamic garb.
The lawyers claimed the cartoons offended Islam but Sawiris said they were just a joke and had no religious dimensions.
Coptic Christians make up around 10 percent of Muslim-majority Egypt's population and have frequently been targeted by Islamic extremists. They also claim they are discriminated against by the state.
In January 2011, a suicide bomber killed more than 20 Christians outside a church in the northern port city of Alexandria, amid accusations by Islamists that the Coptic Church had detained a woman who converted to Islam.