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).
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The term "Vegetable Base" would be construed to describe a food where a vegetable is the primary constituent - such as a "Vegetable Based Soup Stock".
The "Vegetable Base" would be the vegetable component, and would usually (although not always) be a concentrate of some sort.
You're referring to a "cold storage facility", in this case, specifically for vegetables, although the same terminology is used for storing processed and semi-processed meat animals (eg sides of beef, etc.).
Hope this helps!
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The terms packing house or packhouse describe a structure similar to what you are looking for.
A packing house is a facility where fruit is received and processed prior to distribution to market.
(Source: Wikipedia )
Some sources refer specifically to fruit packing or alternatively for meat processing (where is is also called a slaughterhouse ), while others (e.g. see Wiktionary entry ) include other kinds of produce as well.
Wikipedia has a list packing houses in the United States , and most of them have "packing house" as part of the name.
This seems to indicate ithat the term is established in the food industry.
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Wikipedia uses the generic term "produce distribution centre" .
"Produce" is a common and highly standardized term for unprocessed fruits and vegetables on their way to retail.
Here in Ontario we have installations called "food terminals", where produce is sold at wholesale to buyers working for restaurants and markets.
But "produce distribution center" is probably the better generic option.
With "warehouse" the emphasis is on storage, possibly long-term (which would not be the case for produce) and also does not convey the multi-buyer wholesale distribution aspect.
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While not vegetables, grain is stored in a granary .
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How do they refer to big roofed places, in which vegetables, having been brought from fields, are kept before being taken to various outlets to be sold?  I thought "vegetable base" was a good term, but it looks like Google doesn't return many results. Besides, Wikipedia doesn't have an article on "vegetable base"
Is "vegetable base" a common term in English?
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 Wikipedia uses the generic term "produce distribution centre" . Wikipedia uses the generic term "produce distribution centre" . The terms  packing house  or  packhouse  describe a structure similar to what you are looking for.  You're referring to a "cold storage facility", in this case, specifically for vegetables, although the same terminology is used for storing processed and semi-processed meat animals (eg sides of beef, etc.).  The term "Vegetable Base" would be construed to describe a food where a vegetable is the primary constituent - such as a "Vegetable Based Soup Stock "Vegetable base" is incorrect in this context. However, "packing house", "food terminal", "cold storage facility" or "pack house" are al viable terms.
"Vegetable base" is incorrect in this context. "packing house", "food terminal", "cold storage facility", "packing house" or "pack house" are all viable terms.