Biological, physical and chemical science from the 19th century started the process of the "scientification" of medicine , but I would suggest that only with the advent of "evidence based medicine' in the 1980s can medicine claim to be really generally scientific.In particular large scale epidemiology,mediated by powerful statistical computing ,from the 1990s, has made this really practicable.

However, subjective elements will always remain in medical practice so medicine will always remain to some extent an "art".

Medicine is a practice, that is based in knowledge that can be obtained from science and use technology scientifically developed. Medicine is not a science. Historically at the Hipocratic era the origin of diseases stop being considered magical or divine, and a cause was associated with an unbalance at "humours". Directed methodoloy was introduced to balance them in this time. That might be the beginning of the "scientific" approach.