Trade can allow countries to overcome local or regional losses (shocks) to their food supply, but reliance on international food trade also exposes countries to risks from external perturbations. Countries that are nutritionally or economically dependent on international trade of a commodity may be adversely affected by such shocks. While exposure to shocks has been studied in financial markets, communication networks, and some infrastructure systems, it has received less attention in food-trade networks. Here, we develop a forward shock-propagation model to quantify how trade flows are redistributed under a range of shock scenarios and assess the food-security outcomes by comparing changes in national fish supplies to indices of each country's nutritional fish dependency. Shock propagation and distribution among regions are modeled on a network of historical bilateral seafood trade data from UN Comtrade using 205 reporting territories grouped into 18 regions. In our model exposure to shocks increases with total imports and the number of import partners. We find that Central and West Africa are the most vulnerable to shocks, with their vulnerability increasing when a willingness-to-pay proxy is included. These findings suggest that countries can reduce their overall vulnerability to shocks by reducing reliance on imports and diversifying food sources. As international seafood trade grows, identifying these types of potential risks and vulnerabilities is important to build a more resilient food system.