You can do an MBA with a concentration in health - there are few great programs out there. I did my MBA through University of Florida (executive program) with a concentration in healthcare management. I'm applying to a few schools right now to obtain another Masters in Health Informatics and Health Public Policy.
I'm a firm believer that an MBA will not be as effective in your work until you have enough experience. The only exception is what field you're working in - being health - I would expect 3-4 years of management experience to really apply your knowledge. See if your company will pay for you to get your MBA and allow you to use your work as a foundation.
Best of Luck
