According to Eat by Date, it is safe to freeze delivery pizza. Pizza has a short shelf life when it is not frozen or placed in the refrigerator.
Refrigerate delivery pizza for three to five days, or freeze for four to six months. Store delivery pizza in freezer bags or freezer-safe containers before placing it in the freezer. Write the freeze date on the freezer bag or container before storing. When storing pizza in the refrigerator, put it in an air-tight container. If pizza has been left out at room temperature for two hours or more, it should be discarded.