We study the optimal monetary policy response to the imposition of tariffs in a model with imported intermediate inputs. In a simple open-economy framework, we show that a tariff maps exactly into a cost-push shock in the standard closed-economy New Keynesian model, shifting the Phillips curve upward. We then characterize optimal monetary policy, showing that it partially accommodates the shock to smooth the transition to a more distorted long-run equilibrium―at the cost of higher short-run inflation.