You might notice that Prince Prospero shares his name with the main character of Shakespeare's The Tempest. In fact, that's only the beginning of the interesting ties between Poe's short story and Shakespeare's late play.
One nifty connection, which some scholars have taken to be really important, is the mention of a "red plague" in The Tempest. The "red plague" shows up in a curse uttered by the Caliban character (who's kind of a bad guy) early in the play:
You taught me language, and my profit on't
Is, I know how to curse. The red plague rid you
For learning me your language!
(The Tempest, Act 1, Scene 2, lines 437-439)
Now is there any more to this connection than the similarity of "Red Death" and "red plague"? We can't find one, at least not without getting speculative. But it wouldn't be too much of a stretch to suspect the phrase gave Poe an idea, since there are other connections to The Tempest in the story as well.
Most of the other connections are best explored by looking at the similarities between the Prosperos in the two works. To hear more about that, check out our character analysis of Prince Prospero. You might also want to check out the great article "Art and Nature in 'The Masque of the Red Death,'" by Kermit Vanderbilt.