When entering or modifying a listing, there is a field on the Additional Info tab called Display Address on Internet (Y/N):
If you select No for this field, your listing will still syndicate to any authorized sites, but the address of the property will not display. These listings will still appear on sites such as Realtor.com and Zillow if they match the user's search parameters (though not from an address search), but the address information will not be there. It will either say undisclosed Address (on Zillow) or the address section will simply be blank (realtor.com).
Note: setting the Display Address on Internet field to No will not prevent the address from displaying on the MLS. There is no way to hide an address on a listing in Matrix.
*** If you do not want a specific listing to show on any sites (agent/broker IDX, consumer portals, etc.), make sure to put a check in None in the Display This Listing on These Websites field ***
Selecting None in this field will prevent any syndication of the listing.