Heat oil in a deep-fryer or large saucepan to 375 degrees F (190 degrees C).
Mix flour, cornmeal, onion, milk, egg, celery, garlic, and Cajun seasoning in a bowl.
Drop ping pong ball-sized balls of batter, about 5 at a time, into the hot oil. Fry until golden brown, about 5 minutes. Remove hush puppies with a slotted spoon and drain on a paper towel-lined plate. Repeat with remaining batter.