Although not an outright supernatural tale, “The Magic Barrel” has elements of fairy tale magic.  First of all, the title gives us a clue. 

The first hint that “The Magic Barrel” contains elements of fantasy is the first sentence.  In a fairy tale, the first sentence usually begins with “once upon a time” and this story begins with “Not long ago” instead.  When the matchmaker shows up, he “appeared one night out of the dark fourth-floor hallway.”  His appearance seems magical, and throughout the story he seems to appear out of nowhere at night.

The story also includes other elements of a fairy tale.  It is a parable with strong Jewish roots. The young soon-to-be-rabbi Leo finds something wrong with every girl, and he is only interested in marrying because he thinks it will be easier to find a congregation.  The matchmaker keeps his cards with girls on a barrel.

   "The drawers are already filled to the top, so I keep them now in a barrel, but is every girl good for a new rabbi?"

First Leo shoots down each girl the matchmaker brings forward, but then he comes to a beautiful young girl whose eyes are “hauntingly familiar” even though he does not know her.  He thinks she will love him.

How she had happened to be among the discards in Salzman's barrel he could never guess, but he knew he must urgently go find her.

This is another fairy tale.  In most fairy tales, the beautiful princess and the handsome prince find each other.  Leo may be no price, but his princess turns out to be Salzman’s daughter and a prostitute.  He marries her anyway because “he pictured, in her, his own redemption.”  Redemption is another fairy tale element.