We study the impact of 160 increases in state-level minimum wages on the dynamics of prices in local grocery stores. We find that the impact of raising minimum wages on prices is small, significant, and occurs in the months following minimum wage legislation and preceding implementation. Our estimates of the minimum wage elasticity of grocery prices lie between 0.03 and 0.05, and are consistent with a full pass-through of cost increases by firms. Our results suggest that the costs of minimum wage increases are borne by consumers, and in the case of grocery stores disproportionally by the poorest households. We also find that minimum wage hikes significantly raise the probability of price increases, consistent with the predictions of state-specific price setting models. We calibrate a simple menu cost model to match the long run features of our data, and find that the model can fit the short-run response to minimum wage increases.