Mozzarella can be purchased in both shredded and sliced form. Both types can be frozen, although shredded mozzarella may not fare as well as the slices. If you are freezing shredded mozzarella, be sure to use an airtight package. A resealable freezer bag works best. It is a good idea to press out as much air as possible before closing the bag. A straw stuck in the corner of the bag can also help to suck out the remaining air for a sort of DIY vacuum seal. The amount of time the mozzarella is frozen for will affect its texture and flavor.
If your mozzarella is packaged in brine, drain the cheese before placing it into a freezer bag. Freezing mozzarella in its brine can alter its texture, making it slightly crumbly when thawed. Draining it will prevent this effect, while still allowing you to keep the cheese in your refrigerator for later.
If you are freezing slices of mozzarella, lay them flat on a baking sheet and allow them to freeze for at least eight hours. Once the cheese is frozen, remove it from the baking sheet and put the slices into a resealable freezer bag. Be sure to squeeze out as much air as possible and label the bag with a date before placing it in the freezer.