Why is the wicked musical about a woman with green skin ?

Green as in jaded perhaps. 

You’ve seen “The Wizard of Oz” right?  “Wicked” is a prequel to it.  Explains a lot.  Why she is the way she is, why the characters are the way they are and exactly what happens to the witch before and after Dorothy ends up in Oz. The wizard isn’t so wonderful, Glinda wasn’t always nice and Elpheba wasn’t always wicked.

The director wanted to emphasize how evil the witch is visually. The green skin sets the witch apart from everyone else including the good witch.  Viewers / audience members have an emotional reaction to the green skin. 

Because the witch is evil!!!!!!!!!!!!!!!!!!

A wicked musical? This is EXACTLY what punctuation was invented for.

You mean:Why is the "Wicked" musical about ... ?

"Wicked" is a musical that reimagines the life of the "Wicked Witch of the West" before she appears in the first of the Oz novels.  It borrows the skin color from the 1939 "Wizard of Oz" film.  The musical is a fantasy that takes place in the land of Oz, so  Elphaba (the green skinned woman) is not the only character with an odd skin color.

She's a witch.  That's one reason.

I think you would have to watch the musical or read the book to know why a Munchkin would be born with green skin

It's really based on the original book written by Frank Baum.  The movie is an abbreviated version and a variation of the book.

It's a prequel to The Wizard of Oz.  If you've not seen that movie, you should.  It will explain it all!