Healthy nutrition is a very important aspect of health. Therefore, every health care professional should have a good understanding of principles of good nutrition. Depending on a profession, one health care practitioner may need to know more than another. For example, medical doctors or nurse practitioners must know a lot about nutrition, because they treat sick patients whose health problems might be related to nutritional deficiencies. Nurses and dietitians must know a lot as well to be able to guide their patients to better health.
If you are looking into a career in health care, check with the colleges of interests about their program requirements.
I'm assuming you're talking about a medical doctor and not a person who has a PhD in a non-science field.
It most likely depends on the discipline. If the person is studying to become a doctor in a field such as nutrition or food science, I would say they probably take lots of classes about food and nutrition. Whereas if someone is studying to be a podiatrist they might have taken some related classes when an undergrad, but it is probably not a requirement when doing graduate work.
If you're interested in whether a specific occupation requires food and nutrition classes, I'd do some research about that occupation's undergraduate and graduate course requirements at various schools.
Nutrition is not always (and possibly less than optimal) taught in the medical schools as a specific topic. Many leaders who develop medical school curriculae believe that nutrition overlaps with so many other areas that it is covered as part of specific topics. For example, in biochemistry, the pathways medical students learn involve metabolism of the major nutrients -- fat, carbohydrates and proteins -- and vitamins and minerals. Then in physiology of gastrointestinal system, the student learns about digestion and absorption of nutrients. Other systems cover other aspects of nutrition (e.g., in cardiology, lipids are taught, and in pathology, the histology of nutritional deficits are learned). Many of us have advocated for improved and coordinated nutrition for medical students, but further progress needs to be made to enhance this part of the education.
Same applies for students in schools of nursing, pharmacy and dentistry!