One can safely bathe a three week old puppy, but most puppies do not require a bath. Usually, a pup's mother will clean the puppy. A puppy can always just be cleaned with a warm, wet washcloth.
Puppies have natural oils on their skin. This keeps their skin clean, healthy and moisturized. When a puppy is bathed, they lose these essential oils. Most shampoos are made for dogs three months and older and are not appropriate for puppies. When bathing a puppy, keep them warm by using warm water, warm towels and a blow dryer. Certain breeds need to get used to the bathing process at an early age.