I haven't done an international volunteer/internship, but I'm hoping to at some point.
They are available, but many are very expensive. Even the internships are typically unpaid. Expect to drop a few thousand dollars (assuming you're going to be there for awhile). Also, many are of a religious (usually Christian) nature. If you google something along the lines of medical missions premed, medical missions pre-med, medical missions premedical, or medical missions pre-medical, you'll definitely get some hits. I'd post some links, but you'll get the same sites running searches like these. Also, if you have a preprofessional office, they may be able to hook you up.
I know that there are religious medical mission opportunities for premeds in the Philippines and non-religious ones in places like Nepal, India and areas of Africa. That's just the tip of the iceberg. And yes, I realize the irony of using the word iceberg 😛
P.S. Why abroad?