The phrase is quite familiar to me, particularly in the context of telling someone that don't look like they're feeling very well, but I've no idea of its origin.

Perhaps it has something to do with the way fish look when they have ick and are about to take a one-way trip down the porcelain highway? Or three days afterward, when they're floating half-eaten in the tank? They always seem to take on a bit of a greenish hue at that point.