Facebook Timeline for Pages came up with an option, Message Button on Page. This option allows the fans of the page to send messages from your page, which are only readable by the admin of the page. You can disable this option if you are the admin of the page by following the tutorial, after the jump.
By disabling the message option for your page, the members of the fans will not see any message button when they view the page. You can again enable the message option anytime when you want to.
How to Hide Message Button from Your Facebook Page Timeline?
Open your Facebook Page Timeline to hide its message button and scroll up.
Now Click on “Manage” and then on “Edit Page“.
Find the “Messages” option and “Uncheck” the small check box.
Now Click on “Save Changes“. The message button will be hidden from your Facebook Page Timeline.
How to enable the message button on your Facebook Page?
You can unhide/enable/show the message button on your Facebook Page Timeline again by simply “Checking the box” from the Manage -> Edit Page -> Messages.