Aal told al-Masry al-Youm Saturday his department received information that several couples had joined the Facebook initiative.
The unnamed 30-year-old spouses reportedly got the idea from a Qatari man who swapped his wife with others six months ago, al-Masry al-Youm said.
To catch the suspects, police sent a young man and woman posing as a married couple to arrange a meeting to discuss swapping partners. When they met at a local square Friday, police arrested them.
The case is being prepared by investigators to submit to the public prosecutor's office, the Web site said.
In April 2009, a Cairo court sentenced a man to seven years and his wife to three for setting up a similar initiative.