I've frozen shredded mozzarella lots of times and it's always been fine. I usually buy several bags of shredded mozzarella from the store when they're on sale. They're not the best quality mozzarella out there but they are a great option for homemade pizza and dips.
I don't even re-wrap these. I throw them in the freezer when I get home from the store and thaw them later when I need them.