If you get a Masters in Fashion Design do you need to take business courses in order to have your own line of clothing?

It isn't required in the United States to have any kind of degree to own your own business or design products. The business classes might be helpful for you in order to understand some of the details of business. An option I would look into would be a continuing education course at a community or junior college in owning your own business. Check out some books at the library or a bookstore on developing business plans. See what questions you have and go from there. Also, use your professors in the master's program, they have tons of information in their heads. !