If you use the term "myth" loosely, you might apply the Frankenstein myth to the characters, plot, and theme of the play. While the play is called Pygmalion, it seems to have many thematic parallels to Mary Shelley's Frankenstein. In this 19 C. romantic novel, Shelley portrays an overly ambitious scientist, much like Henry Higgins, whose experiments create an anomalous being who as a result has nowhere to go. Like Shelley, Shaw explores the effects of such a creation on both the creator and the creation. We see Eliza transformed from a flower girl to a lady, but this transformation involves far more than a transformation of language and clothes. Like the monster, Eliza becomes much more than her creator bargained for--and as Higgins is reminded by his mother and Mrs. Pearce, he has some responsibility toward her in making it impossible for her to return to the world she has known previously. Just as Dr. Frankenstein abandons his monster, Higgins refusal to acknowledge Eliza as anything more than an experiment deeply wounds Eliza who gradually learns to stand on her own two feet in a world of rigid class distinctions and hypocrisy.
Pygmalion was an artist who created a statue of a woman of great beauty and then fell in love with "her." The goddess of love Aphrodite took pity on him and changed her into a real woman (sort of an antique, feminist Pinnocchio).
The analogy fails to "stick," however, in that in Shaw's work Higgins does not fall for Eliza (Freddy does instead), even though there is indeed a battle of the sexes going on. Moreover, when Eliza is transformed, she no longer finds her place in life, being not really part of one world (social class) or the other. The fate of Eliza is also not conclusive; we can imagine that by her resiliant nature she is indeed destined to do more than simply "fetch" Higgins' slippers - but what?
Some producers of the play revindicated the right to change the ending of the play to be more "Hollywoodian," but Shaw's original version allows no margin for romance between Higgins and Eliza. Thus the allusion to the myth concerns Eliza's transformation from a simple flower girl into a lady, but the analogy stops there.