Another thing going on in this play that is reminiscent of a fairy tale is the nature of the bad guy. In fairy tales, we often have these impossibly nasty characters, like the witch who is going to eat Hansel and Gretel, for example. In this play, we have Shylock who is in some ways a caricature of selfishness and evil with his desire to cut out Antonio's very flesh as payment for the debt.
What a great question! The discussion in response to this statement could go on for some time, but clearly I have to restrict myself to a given number of words in my response, so the short answer is I think that we could argue that elements of this excellent play are reminiscent of a fairy tale.
In particular, it is clear that the presentation of Portia that Bassanio gives us in Act I scene 1 presents her as an impossibly beautiful and an impossibly rich heiress that he hopes to win as if he were Prince Charming. Note how Portia is described by Bassanio as he hopes to persuade Antonio to lend him money:
In Belmont is a lady richly left;
And she is fair and, fairer than that word,
Of wondrous virtues...
Nor is the wide world ignorant of her worth,
For the four winds blow in from every coast
Renowned suitors, and her sunny locks
Hang on her temples like a golden fleece...
The presentation of Portia as fabulously wealthy and wonderously beautiful and virtuous clearly has an element of the fairy tale about it, as does the way in which in a sense Portia is trapped through the test her father has designed to ensure that she marries the right kind of man. Bassanio's triumph in this test has echoes of the handsome prince rescuing the maiden who is trapped, clearly indicating the influence of fairy tales on this play.
Editors Bevington(Bantam edition,1988) and Barnet(Signet, 1987) note the work of theatre man Harley Granville-Barker regarding this matter. For his own introduction, Bevington wrote that "As its name[Belmont] implies, it is on a mountain, and it is reached by a journey across water. It is pure, serene, ethereal. As often happens in fairy stories, on this mountain dwells a princess who must be won by means of a riddling contest." In collections of quotes from Shakespeare one finds "Life is as tedious as a twice-told tale, / Vexing the dull ear of a drowsy man." The plays were first presented as entertainment. Therefore, we can expect to sometimes encounter silly comments, as we do from young children. One might also note that fairies are characters in A MIDSUMMER NIGHT'S DREAM and that Shylock, like Hermia's father Egeus in that play, brings his concerns to the local Duke.