Cats will sneeze. When a cat's nose is irritated and feels itchy, it will sneeze. This is a normal reaction of the body. Cats have sensitive noses, and pungent odors and dusty air can cause nose discomfort and sneezing. If a cat sneezes repeatedly, it may be a sign of respiratory disease or a cold. It is recommended that the owner take the cat to the pet hospital for examination and treatment.