You don't need medical experience to get an MHA. In fact, most healthcare administrators on the more business/financial side don't have any medical experience as practitioners.
What WOULD help you is a few years of business experience. The best thing is getting an administrative position at a hospital or healthcare agency that requires a bachelor's degree, and working for 2-5 years. Then you could not only apply to MHA programs, but also consider MPA programs, MBA programs, and MPH programs with a focus in health policy and management. There are more and more MPA and MBA programs that have a focus on healthcare business, like NYU Wagner's MPA (one of the top healthcare policy/management programs in the country). I feel like an MPA or MBA would make you more versatile than an MHA, but if you really want the MHA then go for that.