Not Medical Advice: The dog will just be fine, as the act is much more natural to the species than you might suspect.
Cuteness.com in its article called Why Dogs Drink Urine, explains:
The Flehmen reaction is normal behavior common in the animal kingdom. In dogs, the Flehmen reaction can involve licking the recently released urine of another dog, then freezing in place for a moment with the tongue extended and curled.
Though bizarre, the dog is placing the other's scent on a spot behind the upper front teeth, where two ducts lead to the vomeronasal organ, which is thought to play an important role in pheromone influences on animal brains and behavior.
While urine drinking poses no health threat to a dog, the repeated behavior may signal a bad habit that needs training.
For further reading, see Slate.com's Dogs, cats, and other animals' flehmen response to smell.
Tip! PerfectPaws.com shares Tips on How to Potty Train a Puppy the Easy Way.