We show that after monetary policy announcements, the conditional volatility of stock market returns rises more for firms with stickier prices than for firms with more flexible prices. This differential reaction is economically large and strikingly robust to a broad array of checks. These results suggest that menu costs—broadly defined to include physical costs of price adjustment, informational frictions, etc.—are an important factor for nominal price rigidity at the micro level. We also show that our empirical results are qualitatively and, under plausible calibrations, quantitatively consistent with New Keynesian macroeconomic models in which firms have heterogeneous price stickiness. (JEL E12, E31, E43, E44, E52, G12, L11)