Technically, no. Most medical schools do not have volunteer service as a requirement to apply to medical school. However, all medical schools highly recommend getting experience doing medical related work before you apply to medical school. In fact, you probably have close to zero percent chance if you have no experience in a health setting.
The reason for this is simple: medical schools cannot know if you are a serious doctor candidate unless you have worked for or with a doctor. How can an applicant be so sure they want to be a doctor if they have never seen a doctor in action?
So although volunteering is not a requirement, many applicants opt to do it because medical experience is pretty much required. You do not have to volunteer for a hospital or health clinic, but you do need to get some experience in the medical field.