We study the productivity effect of the German national minimum wage by applying administrative firm data. At the firm level, we confirm positive effects on wages and negative employment effects and document higher productivity even net of output price increases. We find higher wages but no employment effects at the level of aggregate industry×region cells. The minimum wage increased aggregate productivity in manufacturing. We do not find that employment reallocation across firms contributed to these aggregate productivity gains, nor do we find improvements in allocative efficiency. Instead, the productivity gains from the minimum wage result from within-firm productivity improvements only.