I've always disliked using this kind of structures, "There is A, which is ..." or "There is A, whose ..." One (informal) "rule" of good English style is to eliminate excess words where possible, often by using the right verb:
Iran has a traditional medical system based (primarily) on eating the right foods.
Still, that doesn't answer your question. In addition to your first sentence, which is correct, here are some other possibilities:
... medical system, one of whose bases is eating the right foods.
... medical system whose bases include eating the right foods, (etc.)
... medical system, whose principles are based on such things as eating the right foods, (etc.)
... medical system, the basis of which is eating the right foods.
... medical system, in which eating the right foods is a basic tenet.
... medical system, which is based on eating the right foods.
... medical system, one of the bases of which is eating the right foods.
... medical system, which has as its basis a belief in eating the right foods.
... medical system, where eating the right foods is considered a basic tenet.
and so on. There are many more.
You can see that all of these say much the same thing as my first sentence, but are more "wordy". Again, this is about style not grammar, so there's nothing wrong with being wordy. It's just a personal choice.
Note also the different use of basis and bases (which may be confusing because they sound alike). Basis is singular -- there should only be one basis for something. Bases is plural, for things that are based on various other things.