I study how the production network shapes monetary policy transmission to prices. Using U.S. data, I show that industries farther upstream from final demand exhibit larger cumulative price responses to monetary shocks, while downstream industries absorb shocks through output. A calibrated multi-sector New Keynesian model rationalizes these patterns: upstream sectors, which sell predominantly to other firms, reprice more frequently and therefore exhibit less price rigidity. A counterfactual decomposition of the price response shows that this heterogeneity in price rigidity---rather than cost-cascade propagation through input-output linkages---is the primary driver of the cross-sectional responses. The upstreamness differential is strongly asymmetric, large following expansionary shocks but nearly absent following contractionary ones, consistent with asymmetric price rigidity compounding across production stages. Together, these findings suggest that monetary policy's potency depends on the production network's architecture.