The post-earthquake functionality of hospital systems seriously affects the recovery time of a city, and it is important to quantify the hospital system functionality. This paper presents a method that takes into consideration the post-earthquake medical supply–demand relationship in order to quantify the initial functionality and instantaneous functionality loss of a hospital system under the conditions of an earthquake, which is different from the current quantitative method that takes into consideration only the internal factors of the hospital system. In this method, a geographic information system and an earthquake damage prediction model are first used to obtain the medical supply capacity before and after the earthquake and the medical demand after the earthquake. Based on the results of the post-earthquake medical demand and the distribution of the medical supply capacity, the substitution capacity of medical resources is then calculated. Finally, the substitution capacity of medical resources is used to evaluate the functionality of the hospital system before and after the earthquake. A hospital system of a city in eastern China is considered as an illustrative example, and the impact of changes in the medical supply and demand at different times of the day on the hospital system functionality are analyzed. The results obtained show that the changes in medical supply and demand not only affect the hospital system functionality, but also cause changes in the instantaneous functionality loss of the hospital system after the earthquake. The proposed method can be used to quantify the hospital system functionality and reflect the balance of the medical supply–demand relationship before and after the earthquake, and it can help decision makers in developing a disaster reduction strategy to improve the disaster resilience of the hospital system.