As
@gettheleadout has pointed out,
Monster is an incredible piece of adventure/thriller manga that incorporates medicine (and Nazi eugenics, Book of Revelations/Apocalypse, "Sophie's Choice," psychological conditioning, etc)
Another awesome medically-related manga is Osamu Tezuka's
Blackjack, which makes sense because Tezuka was trained as a physician (but is regarded as the Father of Manga). The author gets deep into the darkness of human intent.
I know that One Piece has Dr. Hiluluk (quack), the old witch lady doctor, Chopper, and Law, but Oda does not have a good concept of science or medicine, which I can forgive him for.