This verse is another play on words. It contrasts the strong (healthy/whole) with weak(sick) in a humorous way. The word translated as "sick" is often translated as a moral condemnation, "evil" but its more general meaning is "having weaknesses." More about the word used for "the sick" in this article.
The term translated as "physician" and "doctor" is better translated as "healer."
Christ's Words in Matthew as a Guide to 40 Days of Prayer.