Neither portion of the sentence can function as an independent clause on its own:
✘ The more ignorant a man is.
✘ The less modest he is.
Since each portion cannot stand on its own, and you cannot have a sentence composed of two dependent clauses, the sentence must be a single independent clause.
In fact, it takes the same essential form as other comparative independent clauses:
You are smarter than me.
The dog is faster than the cat.
Neither of those has a component that can be separated from the rest and be able to stand alone.
If you paraphrase the sentence in question, it actually becomes something like this:
A man's ignorance is in inverse proportion to his modesty.
The construction that uses a comma makes it appear as if one portion is a dependent clause while the other is an independent clause—but that's not the case.
Since it's a single independent clause, that makes it a simple sentence.