Pre Cooking: Prime Rib can be stored in the freezer for 6 months. Prime rib can be stored in the refrigerator for about 3-5 days pre-cooking. (Though it is best to cook right away.) Storing Prime Rib Leftovers: It’s best to finish your Prime Rib the day it is cooked, but if there is some leftover, simply wrap it up in a plastic wrap with some of its jus (cooking juices) and put it in the fridge. It will keep for about a week. But try to eat it before then!