Drug shortage is a global problem, and the development of government-enterprise cooperative stockpiles of drugs in shortage, combining physical and production capacity, has become one of the most important means of coping with drug shortages. However, existing studies have tended to overlook the fact that shortages of Active Pharmaceutical Ingredients (APIs) have become an important constraint on production capacity stockpiling and that the lack of incentives and provisions for coordination of benefits have led to a double marginal effect of joint stockpiling by government and enterprises of drugs in shortage. Accordingly, this study introduced the option contract to the drug supply system composed of government and pharmaceutical enterprises and used the subsidy of API storage in lieu as an important initiative to incentivize the reserve of APIs, to construct a model of shortage drug reserve under the government’s leadership. This study aims to improve the effect of government-enterprise joint stockpiling of drugs in shortage, which is of great theoretical and practical significance. According to the classification of production license types of pharmaceutical enterprises, this study established a three-level supply chain decentralized decision-making model consisting of the government, formulation enterprises, and API enterprises, and a two-level supply chain centralized decision-making model consisting of the government and API Formulation (API-F) integrated enterprises, respectively. By solving the inverse order derivation, the government-enterprise option cooperation conditions and optimal decision-making strategy were derived. The study results showed that: (i) The addition of enterprise API stockpiling mode can help the government conventional reserves, and enterprise production capacity reserves, broaden the way of drug reserves, and improve the effect of government-enterprise option cooperation; (ii) when the probability of drug shortages is high, the government should prefer the cooperation of API-F integrated enterprises, which is conducive to reducing intermediate links and government costs and improving the supply responsiveness to shortages of medicines; (iii) Setting appropriate government subsidies for API storage can incentivize enterprises to stockpile APIs and improve drug production capacity and physical supply response capability. This study took the problem of socialized stockpiling of drugs in shortage as an entry point and explored the problems and solution strategies in the government-enterprise cooperative stockpiling of drugs in shortage, which not only made some theoretical contributions to the application of options contract in the government-enterprise cooperative stockpiling of drugs in shortage but also provided new ideas and theoretical basis for the improvement of the stockpiling work of drugs in shortage.