According to the American Fancy Rat and Mouse Association, mice spend a lot of time cleaning themselves and other mice similar to the way cats do, and therefore they do not need to be bathed. If they look or smell dirty, the cage probably needs to be cleaned, or the mouse is ill. Others suggest cleaning dirty mice by rubbing them with a wet cloth.
If the mouse is very dirty, add a few drops of puppy shampoo to some warm water, and dip the cloth in that before rubbing the mouse down. If shampoo was used, then the mouse needs to be rubbed again with a plain wet cloth to remove the shampoo. Rub the mouse dry with a clean dry cloth.
Regularly cleaning the cage helps keep the mice clean and odor-free. The cage should be cleaned and the bedding replaced at least once a week, preferably more often. It is normal for male mice to have a musky odor, but female mice should have no odor that is detectable by the human nose. Any obvious odor from female mice is probably due to a dirty cage.
If a mouse's odor persists after the cage is cleaned, one should consult a veterinarian.