Out of my nearly three decades of work experience:
I was in a similar situation, i.e. I was an engineer and slowly switched to management/business and see myself as a manager with strong software engineering skills today.
I always recommend people to first learn a technical skill (actually engineering skill), then collect experiences over at least ten years and then learn business, preferably by going through an MBA program.
But, and this is really a BIIIG "but": before entering the MBA program define for yourself absolutely clearly, what your values are (ethical, moral, etc). You must be absolutely clear about these values that you would like to hold dear for quite some time. I suggest to have ethics-based values.
Without the ten-year experience and the ethics-based values, an MBA program (depending, of course, on where you do it) in the end *can* corrupt you, because you start becoming quite cynical during it (my experience is based on many different examples, but suffice to say, that it *can* result in cynicism and then in personal-corruption).
You can meet some quite brilliant people at an MBA-program, but you can also meet all those people who are just there to increase their salaries and to find ways of only making more money for themselves. Your values will help you - and with that, you can also influence the other MBA-participants by actively questioning a lot of what you learn there during the course.
On another note: a lot of those McKinsey, etc, consultants have started consultancy *without* years of experience in actually *doing* the work, because they joined McK right after college. This way they only learn the McK-way, which, IMHO, sucks because it is not oriented towards what you contribute to the society by running a business (the sole purpose) but towards how to make more money for yourself (Google "Up or Out Consultancies").
Good MBAs teach leadership and a lot of practical skills (accounting, book keeping, product, strategy, people management, etc).
Bad MBAs teach how to run up the ladder as fast as possible without considering the (negative) side-effects of your actions. And no, the "Vow to Ethical Behavior" at the end doesn't help at all...