The currency you posted is from an occupied territory, see the related wikipedia link.
If you read carefully, it says: Reichskreditkassen on the bottom, Nazi Germany issued these notes in occupied territories which weren't considered to the Reich's territory.
Note that these notes had completely different rules than real Reichsmarks, for example they were legal tender only in occupied territories, and couldn't be subject of a negotiation inside the Reich. Also the fact that it was independent from Reichsmarks, it added a layer of protection of real Reichsmarks. For example it could have been inflated separately from real Reichmarks. Take a note: 5 Reichmarks in German territories were minted on silver coins (I have one), not notes, an important difference!
Read more interesting facts of your banknote here.
I have only a subjective opinion on why didn't they have Swastika, since the webpages only give clues, not definite answers: The occupied territories had their own currency in this form, maybe this was easier to accept as legal tender than Reichsmarks. It was printed very differently to make it easier to separate from real Reichsmarks. Real Reichsmarks were printed approximately 3:4 ratio while occupation Marks were printed on the whole surface.
But if you check out other - in-Reich - notes, for some strange reason swastika doesn't seem to be overly used on banknotes unlike on coins.