I never want to say you can not do something because we all know as soon as someone says it can not be done someone figures out a way.
However, I do not believe any engineering school worth it salt will not accept someone into a MS Engineering degree programs with a business undergraduate. Engineering MS degrees build on what you learn in the first 4 yrs. Other than the first yr or yr and half Business degrees and Engineering have nothing in common. Because of this you would not have any of the basic information you need to a MS degree.
MBA many times do not build on what you learned in a 4yr degree so have any 4 yr degree will allow you to get a MBA, not true in engineering.
I have BSEE from a top rank Engineering school and went to get my MS in Technology Management (otherwise known as tech MBA) from the top Business school in the country, and I can tell you having the engineering background made business school easy. As it was pointed out if you not strong in math and science going into engineering is hard and you have to be a problem solver. Being a very good problem solver made business school easy and the ability to read data and analysis even better.
Also, unless you're in a specialize field most engineers do not get paid top $, yes there are exceptions but generally you just have to like what you are doing. I working engineering for 15 yrs hit the ceiling unless I want to keep going up the management chain and dealing with managing engineers. So I jumped into the business side and having and engineering degree and MBA allows me to do things and get higher paying jobs than someone with just an business background, excluding working on Wall Street or something like that.