Q: Why can the adjective "afraid" be used this way (before a noun clause) in this sentence? 
A King, whose only son was fond of martial exercises, had a dream in which he was warned that his son would be killed by a lion. Afraid the dream should prove true, he built for his son a pleasant palace and decorated its walls for his amusement with all kinds of life-sized animals, among which was the picture of a lion.
Source: Aesop's Fables

"Afraid" is an adjective in all the dictionaries. And in Oxford, it is clearly indicated "not before noun". Then why can it be used this way in the above sentence?

A: In your sentence the noun that the adjective afraid modifies is king which (the noun) is omitted here.
Your sentence can be read this way:

The king, afraid that the dream should prove true…

So it is not the dream that is afraid.
Note that there is an implied "that" in the original sentence.

A: Be careful when interpreting rules you find in dictionaries (or from the mouths of teachers).
In English, most adjectives can be places immediately in front of the noun they modify:

A large house.
  A good book.
  A red car.

However, with some adjectives this is not done, so the following is wrong:

*An afraid king.

This is what your dictionary tells you. It does not say that afraid can never appear before any noun in any situation! Any time you think you find such a broad, absolute rule, be very, very careful. It is probably an incorrect interpretation!
In your sentence, it is the king that is afraid, not the dream. To be more precise, the adjective afraid is part of an attributive phrase (afraid the dream should prove true), that modifies he (and he refers to the king).
It is interesting to note that afraid actually does appear before what it modifies in the sentence! The comma after true is necessary in this case, in order to separate afraid from he. This sentence would be considered wrong:

*Afraid he built a castle.

We do need the comma:

Afraid, he built a castle.


A: The previous answers are correct.
I'd also point out that your example comes from a story. In literature (both prose and poetry), we often take "poetic license" and bend or break the rules of grammar. We do this because it sounds better for some reason. In poetry/song lyrics, we usually use poetic license to fit a rhythm or a rhyme. Although prose doesn't usually concern itself with rhyme, it does have rhythm and flow. The author (or the editor) probably thought the story sounded better with the suspect* grammar. 
Argh! Y'all are really keeping me on my toes! I can't comment yet, so I'm editing my answer to reply to the comments.
The question poster (poser?) seems to suspect the grammar from the story is incorrect. 
