Vegetable base doesn't work in this context. You would use vegetable base to mean that some product comprised mainly vegetables as in: Our soup has a vegetable base.
Your options are several. Supermarkets store fruits and vegetables in refrigerated warehouses. Individual sections of these warehouses are referred to as storerooms (or sometimes as cool-rooms if kept at low temperature). Such storage centres may be referred to as depots or distribution centres although these words are used for any base away from the hypermarkets/supermarkets they serve.
Farmers keep products in barns (which are big) or sheds (which are small) prior to dispatch. Products stored in rooms underground are kept in cellars.
People keep fruit and vegetables in their pantries unless they need to be kept cool in refrigerators or frozen in freezers.
But the short answer to your question is either warehouses (which are large and may be refrigerated) or storerooms (which are relatively small).