The 52-year-old cleric, who was dressed in civilian clothes at the time, was arrested on Thursday afternoon after multiple citizens reported that a man was walking through the area with his trousers unbuttoned and exposing his genitals to passersby for more than two hours.
Witnesses described the suspect as thin, bearded, dressed in black and wearing a hat.
The man was taken to a police station, where he identified himself as a clergyman.
A case has been filed against him on charges related to insulting sexual dignity.
According to reports, the suspect is a metropolitan bishop of the Patriarchate of Alexandria who maintains an active presence on social media.
The patriarchate said it would provide legal support to the cleric, who is expected to appear before a prosecutor.