According to "KISS Guide to Raising a Puppy," puppies explore the world with their mouths; therefore, puppies will eat or drink anything within reach, including their own urine.
Illness
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According to veterinarian Dr. James Glover, the only medical reason a puppy would drink its urine is if the puppy had a urinary infection and was very thirsty and no other fluid was available.
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Behavior
According to Mike Richards, DVM, urine drinking may be done by bored puppies kept in small cages, such as in puppy mills or pet shops, and may become habit forming.
Preference
Some puppies seem to enjoy the taste of urine and somehow find it rewarding to continue drinking it even when plenty of fresh water is available.
Speculation
Male puppies may taste urine of female dogs to determine whether they are in season. The males may have a very small taste or a long drink.
Significance
According to Mike Richards, DVM, puppies will not get sick drinking their own urine but may get sick drinking urine from other animals. When the puppy urinates, it needs to be immediately distracted so it is not likely to turn and drink.