As clarification we're talking about those common fantasy healing potions that recover health over time and their scientific plausibility. Here are some results from my research on the subject:
Modern medicines are pathetic compared to even the weakest of health potions. Medicines reduce the amount of external influences such as bacteria from slowing down healing process unlike health potions which directly increase the regenerative performance.
Law of conservation is rather problematic. Potions could carry construction materials into body, but larger wounds would require tremendous amounts of matter not obtainable from small dozes. This matter could be drawn from surrounding tissues, but would require obscene amounts of food to maintain physical mass and constant drain would cause serious health problems later in life.
Main problem however would be regeneration. I've never heard of anything which would hasten regenerative speed aside from stem cells but even them wouldn't survive digestion and make it into bloodstream intact.
So to summarize: ...if healing potions were scientifically plausible how would they work?