In Facebook using the Privacy settings you can prevent everyone from seeing your Facebook connection. You can access Privacy Settings by clicking Account dropdown arrow and select Privacy Settings from the list of available menu option.
In Choose Your Privacy Settings page, click View Settings link under Connecting on Facebook section.
This would display the following Privacy Settings.
Navigate to See your likes, activities and other connections section and to prevent everyone from seeing your Facebook connection, change the value from Everyone to Friends Only or you can also Customize your preference by selecting the Customize option.