Well, yes! Dogs can eat honeydew melon. However, you should be careful with the dogs you feed honeydew. Dogs with diabetes should not get this treat. The fruit has so much sugar content, which makes it a bad treat for a diabetic dog. You should also avoid giving too much of honeydew to your dog. He might end up with diarrhea. Honeydew is very nutritious and you should consider giving it to your dog every once in a while.