Current research supports that there are benefits to real ingredients over extruded diets and that there are no significant differences in digestibility between raw and cooked diets for dogs, whereas there may be some potential hazards in feeding raw for both the dogs and pet parent.
It turns out, in moderate amounts, celery is a safe and even healthy food for dogs. Per the AKC, celery is a great source of fiber and potassium. It provides a ton of vitamins including, A, C and K, and it's low in cholesterol and fat.
If you're planning on feeding your dog celery, ensure that it's cut into smaller bite-sized pieces. Keep in mind that cutting them too small may pose a choking risk (especially for smaller dogs). Older dogs may prefer cooked celery to raw - as it can be easier to chew and easier to digest.