Most people know that microwave is short for microwave oven.
In English, we typically refer to things by the noun, not the adjective - for instance, we can call a green umbrella an umbrella, but not just 'a green'. Likewise, adjectives come before the noun in English.
I am pretty sure that microwave is the adjective and oven is the noun, since it is an oven that uses microwave radiation to cook food. Is there a particular reason we call 'microwave ovens' microwaves, or was that just to avoid confusion with a conventional oven?