It sounds like both. Obviously it is physical. It becomes "moral" when you inform others about it. This is because they will have varying opinions.
Gerald - interesting that you should ask the question. Religionists would have it that it's a moral issue with or without the presence of the clap. I think most secularists would look at it as a purely medical issue. In any case it's not really a "dilemma," unless it's one of the newer strains that are resistant to antibiotics.