Heat a small skillet over medium. Add curry powder; cook, stirring constantly, until toasted and fragrant, about 1 minute and 30 seconds. Remove from heat.
Combine sweet potato, yogurt, 1/2 cup water, tahini, lemon juice, ginger, salt, and curry powder in a blender or food processor (blender will yield very creamy results; food processor will yield a coarser texture); process until smooth. Serve cold or at room temperature with crudités.