According to Hamsterific.com, hamsters should not be given baths unless it is absolutely necessary. Hamsters have natural oils on their fur that serve important functions, and bathing a hamster removes these natural oils. Hamsters can also catch colds if they are not dried properly after bathing.
Hamsters typically clean themselves on a regular basis. However, using chinchilla dust once a week can help clean and maintain hamster fur without using water. According to PawNation, keeping the hamster cage cleaned and in a well-ventilated area can cut down on unpleasant hamster odor. However, if a hamster smells extremely bad, it is best to take it to the veterinarian to rule out any health issues.