I believe the quote to originate from Martin Rees, however I cant help but make the point that it is false.

Absence of evidence is in fact evidence of absence. That there is no reliable evidence for God (for example) is in fact a useful indicator that the entity in question may not exist.

Or for a more prosaic example, we have never seen a bird with three wings, the absence of evidence for such critters is therefore indicative of their non-existence.

A better claim would be: Absence of evidence is not proof of absence.

Because whilst it is indeed evidence, it is not proof.