According to WebMD, puppies and dogs shake for a wide variety of reasons. These reasons are often benign but are sometimes an indication of ill health. Puppies shiver or tremble with excitement, fear, while dreaming, when in pain or when suffering from certain illnesses.
The Daily Puppy describes how dogs and puppies move into deep sleep after around 20 minutes of sleep. This sleep phase, commonly known as rapid eye movement, or REM sleep, results in dreaming, which often includes shivering, whimpering, growling, or paddling feet. This is a benign and natural form of shivering for dogs and puppies, along with shaking from excitement. All dogs, but particularly puppies, get excited for a whole host of reasons, from hearing their owners talk to them in silly, squeaky voices to greeting them when they come home. Perhaps the pup can see a squirrel out in the garden that he is simply desperate to go and chase. The anticipation and enthusiasm can cause shivering, which is a perfectly harmless occurrence.
According to Pets Best, shivering is a common indicator of fear or anxiety in dogs, such as during thunderstorms or firework displays, or when the puppy is feeling uncomfortable or anxious. According to WebMD, shaking is also a clear sign of pain or certain health complaints, such as distemper or poisoning. It is also a sign of pain and discomfort, whether from a stomach ache or an injured leg.