Yes, there is ambiguity:
When a sentence containing a clause-modifying adjunct, such as a because
clause, is negated, the resulting example is ambiguous.
Because clauses and negative polarity licensing
The paper uses the terms "Negated Head" and "Negated Adjunct" to describe the two readings:
NH: You are not hired and the reason is you are qualified.
NA: You are hired but not because you are qualified.
In the NH readings, it is the head proposition which is negated. In the NA readings, it is the relation introduced by the adjunct which is negated.
The ambiguity can be eliminated by rewording the sentence. The NA version is fine, but the NH one is awkward. Instead, try inverting the sentence:
Because you are qualified, you are not hired.