c. 1200, "medical treatment, cure, healing," also (early 14c.) "substance used in treatment of a disease, medicinal potion or plaster," also used figuratively of spiritual remedies, from Old French medecine (Modern French médicine) "medicine, art of healing, cure, treatment, potion" and directly from Latin medicina "the healing art, medicine; a remedy," also used figuratively.
This is perhaps originally ars medicina "the medical art," from fem. of medicinus (adj.) "of a doctor," from medicus "a physician" (from PIE root *med- "take appropriate measures"); though OED says evidence for this path is wanting and suggests derivation directly from medicus. The sense of "practice, theory, or study of curing, alleviating, or preventing disease in humans" is from mid-14c.
The figurative phrase take (one's) medicine "submit to something disagreeable" is recorded by 1865; that of dose of (one's) own medicine is by 1894. Medicine show "traveling show meant to attract a crowd so patent medicine can be sold to them" is American English, 1938. Medicine ball "stuffed leather ball used for exercise" is from 1889.
It is called a "medicine ball" and it got that title from Prof. [Robert J.] Roberts, now of Springfield, whose fame is widespread, and whose bright and peculiar dictionary of terms for his prescription department in physical culture is taught in every first-class conducted Y.M.C.A. gymnasium in America. Prof. Roberts calls it a "medicine ball" because playful exercise with it invigorates the body, promotes digestion, and restores and preserves one's health. ["Scientific American Supplement," March 16, 1889]