Heat vegetable oil in a skillet over medium heat; cook and stir onion and celery in the hot oil until softened, about 10 minutes. Season with salt and black pepper.
Mix onion mixture, water, diced tomatoes, coconut milk, tomato sauce, and tomato paste together in a large pot; bring to just a boil. Reduce heat and simmer until heated through, 15 minutes.
Pour soup into a blender no more than half full. Cover and hold lid down; pulse a few times before leaving on to blend. Puree in batches until smooth.
