By default, people you do not know can send you messages on Facebook. But you can adjust your privacy settings to stop people who are not your Facebook friends from sending you a message. When a person who is not your friend accesses your profile, the option for sending a message is not presented. Edit the privacy settings for your Facebook account to suit your needs.
Access Facebook in your Web browser and log in to your account.
Click "Account" in the upper-right menu, then click "Privacy Settings" in the drop-down menu.
Click "View Settings" under "Connecting on Facebook."
Click the drop-down menu next to "Send You Messages" and select "Friends Only." Your new profile settings will be saved when you navigate from the page.