Yes, some dogs have a soft spot on their heads. This spot is called an open fontanel, and it occurs when the bones of the skull fail to calcify or fuse completely. If your puppy has an open fontanel, your veterinarian should evaluate him for other congenital defects.
The open fontanel is at the top of the head, and it is a relatively common occurrence in some toy and small breeds such as the Chihuahua. Most puppies are born without the skull completely fused, but it generally closes over time. Organizations like the American Shih Tzu Club state that most open fontanels close by 4 months of age. If your puppy's does not, care must be taken, as the brain is unprotected at that spot. His activity made need to be limited to prevent falls or other injury, which could be life-threatening. Affected pets should also not be bred.
Elizabeth Muirhead is a practicing veterinarian with an undergraduate degree in biological sciences. She has real-world experience with the husbandry, grooming, training and feeding a variety of household pets.