Recent events have reignited concerns about the financial stability implications of monetary policy. We show empirically that monetary tightening exacerbates financial stress after supply shocks, through declines in asset prices, bank equity and increased run risks. We then develop a tractable model in which intermediaries face occasionally binding leverage constraints and endogenous risks of runs, while producers face price adjustment frictions. Interest rate tightening, by lowering asset prices, exacerbates both financial distortions when intermediaries’ equity is sufficiently low. We use the model to characterize the constrained efficient use of interest rate policy, credit policy, equity injection, macroprudential policy and deposit insurance during periods of supply-driven inflation and fragility. When other tools are costly, optimal monetary policy tightening should be less aggressive in the presence of financial fragility. If other tools were not costly, the right combination of tools could perfectly separate financial stability from price stability objectives.