Shaimaa Ahmed, a 25-year-old singer better known by her stage name Shima, appears in the video in her underwear singing while suggestively eating an apple and a banana before a class of young men.
The video created a stir on social media in conservative Egypt and was discussed on TV talk shows.
The officials said Shima was arrested last week following a flurry of complaints. She was remanded for four days. Prosecutors on Monday ordered her detained for seven days.
The officials spoke on condition of anonymity because they were not authorised to brief the media.