Answer: You don’t have to refrigerate oranges, but you'll be able to enjoy them much longer if you do. As the Florida Department of Citrus points out, oranges don’t ripen any further once they’ve been picked and the refrigerator is the best place for maximimizing their shelf life.At room temperature, oranges usually keep for up to one week — in your fridge, they'll generally stay fresh for up to three weeks.Once you've peeled or cut into an orange you should refrigerate any leftovers right away.Wrap the cut fruit tightly with plastic wrap or store in an airtight container and use it within three or four days.nswer: You don’t have to refrigerate oranges, but you'll be able to enjoy them much longer if you do. As the Florida Department of Citrus points out, oranges don’t ripen any further once they’ve been picked and the refrigerator is the best place for maximimizing their shelf life.