While it is true that books are more likely to be written by educated people, there is no specific requirement. Generally it comes down to your writing skill and style. At a bare minimum, you must be able to write clearly, grammatically and correctly in your chosen language. Despite Faulkner, your writing must be free of spelling and grammar errors or no editor will read it. If you went to a good high-school, then you might have those skills without higher education. Still, some classes wouldn't hurt.
To become an author, you must have tremendous self-discipline. Writing is hard work. It takes dedication, persistance and concentration. Unless you work for a newspaper, there won't be anyone to tell you what to do or when to write. There are lots of people who have written only the first chapter of a book. This is not a matter of education but of personal character.
Now, if you want to be an author and need to know what kind of education will help... that's a different question. Generally you need to take courses that make you write; the more practice you have the better. Of course there is always English or literature (or even English literature). But subjects like history or philosopy also require a lot of writing. It is very helpful to take any creative writing courses you can.
Of course, there is a difference between an author and a published author. Having a written a good book is no garuntee that you can get it published (although the internet is making it easier). Publishers are very conservative: the best way to get published it to already be published. A number of very famous books were published posthumously. So don't expect to wave a manuscript and suddenly be on the best-seller list. However, for the persistent who are willing to take advice, it can be done.
