I am American girl with Business degree and am interested in working in Japan. Do I need to know fluent ...?

Not really if you can convince an American company to send you to Japan for business with no special skills. A business degree is a dime a dozen. I and many of my friends have one. What skills do you bring to the table that qualifies you to work in a particular foreign country of which you have no business knowledge of or speak the language. If you ,were talking MBA you would have a better shot but what area of expertise endemic to Japan do you have. Especially as you can't speak Japanese let alone read or write or be familiar with their specific business environment. Of course you can try, stuff happens, but by being here and learning more about Japan an its language and business practices you have a better shot. But then you won't get hired on an expat package which is more lucrative than a local package. There are other jobs I am sure you are aware of that will get you a visa...like language schools and such but as a business person sought after by a large company you have to tell them what in particular you can bring to the table vs people who have degrees related to the Asian business environment/language/and culture, specifically Japanese. But hey you will hear about exceptions. Good Luck.

No you don't. I am an American working here. I didn't know a single word when I first came here. It doesn't matter in some companies. Of course, it helps to be conversational.

well DUH of course you do unless somebody in JAPAN speaks ENGLISH!!!!!!!!!!!!!!!

You don't need to be fluent if you just want to teach English... But if you want a real job, you need to contribute to the company, and the only way you can do that is to know the lingo.