This sentence looks like either a coordinating conjunction and has been omitted, or not is acting as a coordinating conjunction. If we assume that there is a coordinating conjunction there, these rules explain when a comma is necessary.
Rule: Use a comma before a coordinating conjunction that joins two independent clauses.
She purchased the car, but she declined the extended warranty.
Rule: Do not use a comma before a coordinating conjunction if the sentence contains only one independent clause.
She purchased the car but not the extended warranty.
It seems to me that the second rule applies, so no comma is required. But maybe the comma is standing in for that missing coordinating conjunction? Even in well-documented situations, punctuation can be quite flexible: in a case like this, where no documented rules apply exactly and either version is perfectly understandable, it's probably more a matter of personal style than anything else.