Yes, you can freeze cheese, but the texture will change. The suitability of freezing depends on the type of cheese and its intended use.
Hard cheeses like cheddar and parmesan freeze well. Soft cheeses can be frozen, but their texture will suffer more noticeably.
Freeze unopened blocks in their original packaging. For opened blocks, use a resealable plastic bag with as much air removed as possible.
Shredded cheese can be frozen in a resealable plastic bag. Pre-shredded cheese can be frozen in its original container or bag.
Freeze sliced cheese in its original package. For self-sliced or deli cheese, use a plastic freezer bag with parchment paper between slices.
The texture of cheese changes when frozen. Hard cheese still melts well, while soft cheese is best used in baked goods.
Thaw cheese in the refrigerator and use as soon as possible. Some frozen cheese, like shredded mozzarella, can be used directly from the freezer.