Monetary policy affects the degree of strategic complementarity in firms' pricing decisions if it responds to the aggregate price level. In normal times, when monopolistic competitive firms increase their prices, the central bank raises interest rates, which lowers demand and creates an incentive for firms to reduce their prices. Thereby, monetary policy reduces the degree of strategic complementarities among firms' pricing decisions and even turns prices into strategic substitutes if the effect of interest rates on demand is sufficiently strong. We show that this condition holds when monetary policy follows the Taylor principle. By contrast, if the equilibrium is indeterminate, because monetary policy violates the Taylor principle, or in a liquidity trap where monetary policy is restricted by the zero lower bound, pricing decisions are strategic complements. We discuss the consequences for dynamic adjustment processes after shocks and some policy implications.