Peel and roughly chop the ginger. Trim the celery and cut it into 5 cm (2 inch) lengths. Juice the tomatoes, carrot, garlic and horseradish with the ginger and celery.
Transfer the juice to a food processor or blender, add a couple of ice cubes and process briefly.
Pour the juice into a small glass, garnish with celery slivers, if liked, and serve immediately.