Because it can be a sick color like an infection and envy is a sick emotion, perhaps. This requires some research and I am just the person to do that. I like this question. Maybe Tink made you think.
Ooooh, good answer, Kay. But the first answer is also not far off. According to this Biblical scholar, Mary Kassian, the origin of the phrase is something like this:
Why is Envy Green?
Why do we turn “green” with envy? In antiquity, the Hebrew word for envy, qinah, referred to the burning color in the face produced by a deep emotion. The Greeks believed that jealousy was accompanied by an overproduction of bile, lending a yellowish-green pallor to the victim’s complexion. In the seventh century B.C., the poetess Sappho used the word “green” to describe the face of a stricken lover. After that, the word was used freely by other poets to denote jealousy or envy. The most famous such reference and the origin of the term “green-eyed monster” is Iago’s speech in Shakespeare’s Othello: “O! Beware my lord, of jealousy; it is the green-ey’d monster which doth mock the meat it feeds on.”
We have changed much in the past 2000 years, since "green" today is a very good thing, a sign of health, WEALTH, and being environmentally conscious.