Climate-induced shocks in grain production are a major contributor to global market volatility, which creates uncertainty for cereal farmers and agribusiness and reduces food access for poor consumers when production falls and prices spike. Our study, by combining empirical models of maize production with future warming scenarios, shows that in a warmer climate, maize yields will decrease and become more variable. Because just a few countries dominate global maize production and trade, simultaneous production shocks in these countries can have tremendous impacts on global markets. We show that such synchronous shocks are rare now but will become much more likely if the climate continues to warm. Our results underscore the need for continued investments in breeding for heat tolerance.