Strictly speaking, all engineering disciplines require more math than most other fields. In my own case, I've found that day-to-day work activities don't usually require much math, but on the occasion when they do, it's absolutely necessary to get the job done. Now, if you're asking if a lot of math is required to graduate with your engineering degree, absolutely. But if you find this daunting, I'd recommend getting a tutor, since a friendly face helping you with math from a fresh point of view might be all you need to help you see the subject in an enjoyable light rather than drudgery. Give it a shot!
From my experience at Penn State, any engineering degree is going to require a lot of "math" specific courses; I took 6 when I graduated in Aerospace Engineering (listed below). However, the physics courses that you will be required to take will also be very heavy in math. I am not sure how math heavy the actual biomedical engineering courses will be, but I would imagine there would be quite a bit involved, since you are required to take so many foundational courses. Once you have these courses under your belt and you understand the math well, most courses after that are just a matter of application of principles you have learned. Check out this link to see exactly what courses you would need to graduate in Biomedical Engineering from Penn State:
This will be a great reference for you no matter where you choose to go. Each program will have many similarities.
Math I took:
Calculus I, II, and III
Ordinary Differential Equations