Hi! Well, there isn’t really one direct way into the profession. I’d really recommend this page on the Association of Medical Illustrator’s website:
That will give you a really good overview of what type of education is expected in the field. Some of my classmates went to specialized undergraduate programs like at Iowa State (http://www.bpmi.iastate.edu/) and Virginia Commonwealth University (http://arts.vcu.edu/communicationarts/scientific-and-preparatory-medical-illustration/), but a whole bunch (myself included) majored in either art or science with a minor in the other, and selected classes that were required for the graduate programs.
Most people in the field have an advanced degree so knowing what skills and knowledge those programs look for is a great base to use when figuring out where you want to do your undergraduate work. And while each school will give you the basic skill set you need to be a medical illustrator, each is very different in their structure and the techniques they’ll teach you. This is just kinda general stuff, but if you have any more specific questions I’d be happy to answer. :)