It is alleged that the Facebook page in question is a forum for a group of gay men who fantasise about having sex with monks, or men dressed like them.
It appears to publicise a pornographic video featuring what looks like a Buddhist monk engaging in sex.
According to one source the Monk appears to come from the North of Thailand while the other man featured in the video is from the Taling Chan district of Thailand's capital, Bangkok.
He claimed the man who looked like the monk in the video clip lives in the North, while the novice lives in Taling Chan district of Bangkok.
The group has around 800 members and at this stage it is unclear who set up the group or where.
The CSD said they received the complaint on Tuesday from Songkran Atchariyasap, who heads a network that investigates acts which it claims harm the nation, religion and the royal institution.
Songkran said he had provided the CSD with a copy of the two-minute long clip featuring the offending sex scene, along with the results of his own investigation into the Facebook page, according to the Bangkok post.