In Canada health care is publicly funded, so getting into their BA world involves having a mixture of IT health care and government, experience (probably in that order of importance). I know some BA's working in the health care sector are former doctor's and nurses.  That said, it's not realistic to expect people to have a great knowledge of health care going in, and most good BA's can be effective in any domain. 

I'd take a look at what big IT initiatives are going on in your health system and learn as much as you can.  For instance, in Canada provinces are moving along the development path of Electronic Health Records (EHR).  If you google 'electronic health record alberta' with tech terms (eg. it process, architecture, system, infrastructure, etc.) you'll find that there's a fair bit about the overall architecture of the system.  Having an understanding of how your health system is evolving plays a big part.  You don't need any medical background to be able to excel in this vertical in my opinion, although it will help with the learning curve for some of the jargon they use.