Do you mean medicine as a practice or do you mean actual medicines, as in remedies for ailments? I can answer the latter for you.

I read an article for my qualifying exams about a spectral analysis of a Roman remedy. The citation is: Ilani, S., Rosenfeld, A., & Dvorachek, M. (1999). Mineralogy and Chemistry of a Roman Remedy from Judea, Israel. Journal of Archaeological Science , 26, 1323-1326 This is my summary of the article and its research from my unpublished exam: [The scholars] examined the contents of a tube found in a Roman tomb from the Judean mountains. They analyzed the powdery contents spectroscopically, and found that it contained a mixture of minerals, mainly hematite and malachite. The tube shape indicated that it was intended for applying semi-solid medicines externally, and probably the powder inside had been mixed with a now-decayed adhering medium, such as beeswax, fat, or honey. The authors consulted Roman medical texts, and found that this medicine would have been prescribed to treat hemorrhage and ulcers, and probably would have even been beneficial.

There at least is one kind of medicine that was used by Romans, and others would have been similar.