This is entirely setting dependent. It is entirely possible for a setting to be structured so that magical healing is relatively common and strictly better than mundane methods. In that case, there would be very litle reason for nonmagical healing, other than first-aid to stabilize someone until they get to a healer or for the very poor who may rely on someone with an herb garden and some knowledge that may or may not be actually true. These settings address it by virtually getting rid of professional, non-magic using healers.
Now if you want to create/tweak a setting so that non-magic healers can coexist meaningfully with the magical kind, then you need to limit magic in some way.
Limits on how much magical healing
As others have mentioned, the most straightforward way is to make it existing, but rare. In that case, you might have access to a healer in a major city, but out in the field you are relying on your friendly medic.
Another way is to make it much more expensive than non-magical. It may require rare and precious ingredients that get burned up in the process. It may come at a high cost to the healer himself, in fatigue or in risks of things going wrong or even in taking a portion of the damage healed himself.
But probably the best way is to limit what magical healing can do. Patch up flesh wounds so you can keep fighting? Sure, say a few words and it's done. Broken bone? Maybe, but you can only try once and its not reliable. Ooh, you have internal organ damage. Now, magic might stabilize you but you're going to need surgery, soon. Something got infected? You need antibiotics, and the right antibiotics, to a medic you go.
Make them cooperate
Another interesting approach is to make them complementary. Mechanically, this could be as simple as giving a major bonus to the roll when they work together, or you can only roll for magical healing once for a given wound and only do first-aid once, but you can do both for the same wound.
In terms of story explanation, you get things like magic can make that flesh wound close, but if it has not been properly cleaned out by the medic first it will get horribly infected. Magic can make that bone heal in minutes instead of months, but if a medic hasn't properly set it first it will heal horribly mangled and cause problems for the rest of that persons life.
Treating a disease might involve magic suppressing the immediate symptoms and a medic giving alchemical concoctions to actually speed the full recovery.
When faced with something new, they might also need to work together on the research, with the magic user providing knowledge of arcane energies and the medic providing knowledge of the body and bacteria. In real life, serious medical progress often involves lots of specialists working together, many of them may be statisticians or even physicists for certain areas of medicine rather than yet more doctors. There is no reason you wouldn't need more than one type of specialist to cure a new disease
In this way, you would expect to find medics working alongside magical healers and have a built in reason to have both.