Back in 1986, there was an article published titled, "Administrative medicine: a new medical specialty?" The health care system has changed dramatically since then and the definition of "administrative medicine" continues to evolve as more physicians leave the bedside to pursue careers in business and administration. In 2009, Dr. Arthur Lazarus, a board member of the American College of Physician Executives, published a paper titled, "Professional and career issues in administrative medicine."
If you're interested in a career in administrative medicine, I would suggest the following:
First, join the American College of Physician Executives (ACPE) and the American College of Healthcare Executives (ACHE) and get involved in these organizations.
After you've gotten involved, consider whether you'll want to pursue a master's degree. Many physicians choose to get either an MBA or an MMM (master of medical management) to strengthen their credentials, solidify their knowledge base, and expand their network in the world of medical administration.