Why the Name?
It is called a "medicine ball" and it got that title from Prof. 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]
The name "medicine ball" is a play on the American Indian device, the "medicine bag" which the medicine ball resembles.