Store the artichokes in the refrigerator. This vegetable should be loosely wrapped in a plastic or aluminium film. Fresh vegetables last up to a week but it is better to consume them as quickly as possible. Cooked artichokes should be cooled completely before storing in the refrigerator, if they are kept for more than a day or two. Do not place washed artichokes in the refrigerator for storage as the moisture causes the vegetable to spoil. Ensure raw or cooked artichokes are dry before storing in the refrigerator..