If your dog rubs her muzzle after eating, she might be expressing pleasure, cleaning her face or trying to relieve discomfort triggered by a food allergy or other irritant. Observe her behavior after meals and rule out a medical cause for the muzzle rubbing to determine the reason she does it.
Learn Dog Language
Some dogs complete an entire routine of expressing delight after a meal. More rarely, a dog might give these signals while you're preparing her food. The happy signals may start with your dog rubbing her nose against the floor, rolling on the floor on her back and then rubbing her muzzle. All of this expresses that a good thing happened or is happening. Some dogs rub their chest on the floor as well as their muzzles. Rubbing her face from eye to nose with her paw might come at the end of the full ceremony or she might perform this one gesture of dog sign language to communicate her pleasure.
Confirm a Contentment Ceremony
Psychologist Stanley Coren calls these specific dog behaviors a "contentment ceremony" in his book "How to Speak Dog: Mastering the Art of Dog-Human Communication." He notes that dogs also perform this ritual after a happy event such as a favorite outing, so the signals aren't exclusive to eating. Notice if there are other times your dog rubs her muzzle and if she does any of the other contentment ceremony movements. In this way you might be able to confirm that she's using the muzzle-rubbing to express pleasure after her meals.
Look at That Clean Dog
Dogs sometimes rub their faces to clean them, even licking their paw first the way a cat does. Paw licking is common grooming behavior. Some dogs rub their muzzles on the carpet, your couch or on the grass possibly for grooming, to remove food stuck in their teeth or simply because it feels good. With fewer means for cleaning their faces and teeth than people have, dogs rub with their paws or on objects. Some dogs are more fastidious than others or feel uncomfortable if there's food or moisture on their muzzles. You might wipe her face after meals with a damp washcloth to see if she likes it.
Rule Out Other Causes
If she only rubs her muzzle after she eats and possibly after other things she enjoys -- and there are no signs of irritation such as watering eyes, swelling, sores on her gums, or flinching if you touch her muzzle -- odds are she rubs her muzzle to express pleasure. If your dog persistently rubs her muzzle, it could be a sign of a medical problem such as a skin, gum or tooth condition, allergies or other irritant. Food allergies and other problems that can make her mouth, nose or muzzle uncomfortable are fairly common in dogs. See your veterinarian for diagnosis and treatment.