After a user of the social network was befriended by a girl, a doctored image of the victim was sent to his employer's Facebook page.
The image showed the victim engaging in a sexual act in the presence of a child, said police.
He then received a message saying, unless Â£7,500 was paid, the photograph and images like it would go viral.
The advice from officers is to never accept a friend request from anyone you do not know and, if you are subject to any criminal activity, to contact them.
Cheshire Police have issued a warning about an online sex scam which involved an attempted blackmail on Facebook.