Etymology of "medicine" and its Native American usage
Solution 1:
Medicine comes from the Latin [ars] medicina, from medicus (physician), from medeor (to heal). The root mad- or med- occurs in several languages: middle Persian madha (medical science, wisdom); Sanscrit medha (intelligence, wisdom); ancient Greek medos (advice), medomai (to think about). Consider also words such as meditate, from the Latin meditari.
I'd venture to say that med- or mad- was a paleo-indoeuropean root related to considering, advising or knowledge. In archaic times, giving advice on how to treat illnesses must have been the prerogative of the learned man, the priest. It turns out, then, that using "medicine man" for "shaman" might have been more appropriate than it seems at first.
Solution 2:
It appears this is derived from the French term for "doctor" (médécin). See Encyclopedia of Native American healing By William S. Lyon.
Medecine Man The most popular term applied to Native North American healers ... The origin of the term can be traced at least to the time of the French Jesuit missionaries during the seventeenth century. Among the Huron, Mangagnais, Ottawa, and other inhabitants of New France, the missionaries wrote of the healers, the hommes-médécins ...
Solution 3:
According to the OED, "medecine man" is a calque (loan translation) of Ojibwa mashkikiiwinini "physician" (mashkiki "medicine" + inini "man"). The first citation is 1801.
Solution 4:
Interesting the etymology doesn't seem to go anywhere. ie. medicine from the latin medica, meaning medicine = very helpful!
This article discusses it, http://www.ncbi.nlm.nih.gov/pmc/articles/PMC195119/pdf/mlab00237-0040.pdf
The medicine man usage for shaman/healer is from 1800 apparently and is presumably either an native term based on it being doctors that the white people go to for help - so a doctor was the white man's shamen and the definition of doctor was a medicine man.
Or an English invention for what they thought shamans were doing - and some author decided to render it in simplified "native speak".
Solution 5:
Disclaimer: I know nothing about Latin.
But regarding the etymology of medicine from Latin medica this Perseus Project entry is very interesting and seems to indicate that it is derived from medeor and is related to the Greek μαθήσιος - the act of learning, acquiring knowledge.