At the very least, you'll need a ledger strip against the wall to support the back of the counter. Hopefully the false front is structurally sound enough to support the front edge of the granite. If you've got that much then you've got essentially the same support structure that you'd have with a complete cabinet.

jon1270..thanks for responding...my concern is support for the sink as well as the granite...do I need to build a support "inside" for the sink? Thanks!

Well, there are a variety of ways you can support an undermount sink. Sometimes they get glued directly to the underside of the granite, sometimes they are fitted into a sheet of plywood that sits on top of the cabinets. I don't do a lot of kitchen work so I can't easily say which approach will be best for you, but I'd start by figuring out exactly where that sink need to be within the cabinet -- not just laterally but how far back from the front edge to allow a wide enough swath of granite in front, and how far away from the wall to allow room for whatever faucet you're using. Also, figure out whether your particular granite installation will need to have a layer of plywood underneath. Once you know where the sink needs to be, it shouldn't be too hard to imagine a structure that will support it in that position. I don't think there's a single correct way to do it.