Look up a few BioE MS programs and what classes they require as prereqs. It's usually pretty lenient on requirements, but you have to know what they are instead of guessing. Academics - Master - Admission Requirements - Department of Biomedical Engineering - CCNY - CUNY
Here's one list I quickly Googled. Don't take it as a rule, but a guideline. A statics, materials, thermo, fluids, and a few bio courses are all helpful. If you can't get all of them, you can certainly learn some of it on your own and some of it before admission. Keep in mind you won't be working with everything but with just a certain part.
If your EE program focuses on mechanics, you should be fine. If not, you will have some work to do, but it's still doable.