I found evidence for the first part of the quote, but not the second, here in Table Talk:
I maintain that Satan produces all the maladies which afflict mankind, for he is the prince of death. St Peter speaks of Christ as healing all that are oppressed of the devil. He not only cured those who were possessed, but he restored sight to the blind, hearing to the deaf, speech to the dumb, strength to the paralytic; therefore I think all grave infirmities are blows and strokes of the devil, which he employs as an assassin uses the sword or other weapon. So God employs natural means to maintain the health and life of man, such as sleep, meat, drink, etc. The devil has other means of injury; he poisons the air, etc.
A physician repairs the work of God when damaged corporally; we, divines, spiritually; we mend the soul that the devil has spoiled. The devil gives poison to kill men; a physician gives theriacum, or some other drug, to save them; so the creature, through creatures, helping creatures. Physic has not its descent and origin out of books; God revealed it; or, as Syrach says: “It cometh from the Most Highest; the Lord hath created medicines out of the earth.” Therefore we may justly use corporal physic, as God’s creature. Our burgomaster here at Wittenberg lately asked me, if it were against God’s will to use physic? for, said he, Doctor Carlstad has preached, that whoso falls sick, shall use no physic, but commit his case to God, praying that His will be done. I asked him: Did he eat when he was hungry? He answered, yes. Then, said I, even so you may use physic, which is God’s creature, as well as meat and drink, or whatever else we use for the preservation of life.
There's more on the subject of physicians here,
The physicians in sickness consider only of what natural causes the malady preceeds, and this they cure, or not, with their physic. But they see not that often the devil casts a sickness upon one without any natural causes. A higher physic must be required to resist the devil’s diseases; namely, faith and prayer, which physic may be fetched out of God’s Word. The 31st Psalm is good thereunto, where David says: “Into thine hand I commit my spirit.” This passage I learned, in my sickness, to correct; in the first translation, I applied it only to the hour of death; but it should be said: My health, my happiness, my life, misfortune, sickness, death, etc., stand all in thy hands. Experience testifies this; for when we think, now we will be joyful and merry, easy and healthy, God soon sends what makes us quite the contrary.
When I was ill at Schmalcalden, the physicians made me take as much medicine as though I had been a great bull. Alack for him that depends upon the aid of physic. I do not deny that medicine is a gift of God, nor do I refuse to acknowledge science in the skill of many physicians; but, take the best of them, how far are they from perfection? A sound regimen produces excellent effects. When I feel indisposed, by observing a strict diet and going to bed early, I generally manage to get round again, that is, if I can keep my mind tolerably at rest. I have no objection to the doctors acting upon certain theories, but, at the same time, they must not expect us to be the slaves of their fancies. We find Avicenna and Galen, living in other times and in other countries, prescribing wholly different remedies for the same disorders. I won’t pin my faith to any of them, ancient or modern. On the other hand, nothing can well be more deplorable than the proceeding of those fellows, ignorant as they are complaisant, who let their patients follow exactly their own fancies; `tis these wretches who more especially people the graveyards. Able, cautious, and experienced physicians, are gifts of God. They are the ministers of nature, to whom human life is confided; but a moment’s negligence may ruin every thing. No physician should take a single step, but in humility and the fear of God; they who are without the fear of God are mere homicides. I expect that exercise and change of air do more good than all their purgings and bleedings; but when we do employ medical remedies, we should be careful to do so under the advice of a judicious physician. See what happened to Peter Lupinus, who etc.
So he did say things of that sort, but his main insult was that they are "far from perfect".
He reserves the worst, "fellows ignorant as they are complaisant" for physicians who let their patients do whatever they want, not for physicians who think that ilness has natural causes.