From what I've heard it is definitely possible. Generally graduate schools don't care about what your "major" was in undergrad; they care about whether or not your classes adequately prepared you for the field in which you are applying and your performance in those classes. I was looking at doing an MBA a couple years ago, but I switched to engineering. I would suggest taking a few entry level classes in management, accounting, finance, and/or economics and getting A's in them. This should be enough to show that you are savvy in business as well as your major field.
Actually, a lot of MBA programs like to see a few years of work experience before you apply. That's not to say that you couldn't get in right out of undergrad, though.