The start of the full-scale Russian-Ukrainian war caused the largest wave of migration in the 21st century. More than five million Ukrainian citizens left for EU countries within a few months of the start of the conflict. The purpose of this paper is to forecast the level of health care expenditure in Ukraine for 2023–2024, considering the scale of migration and the fall in the level of GDP. The authors propose three scenarios for the development of Ukraine’s economy in 2023–2024, taking into account changes in the age structure of the population, migration, and the amount of health care expenditure: (1) Pessimistic, in which economic growth will resume only in 2024, with a GDP rise of 5.6%, provided that the war concludes at the end of 2022. Under this scenario, inflation will be about 21% in 2023–2024, a slight decrease compared with the previous year. Some 12% of the population of Ukraine will have emigrated, resulting in a corresponding 12% drop in health care expenditure in 2023–2024. (2) Basic (realistic), in which economic growth will be about 5% in 2023–2024, inflation will be under 10%, and migration will have accounted for 5% of the country’s population. Under this scenario, there will be an increase in health care expenditure of more than 40% in 2023–2024. (3) Optimistic, according to which rapid economic growth is expected in 2023–2024, inflation will not exceed 7%, the majority of those who left Ukraine in the early months of the war will return, and health care expenditure will increase by more than 70% in 2023–2024. The methodology of forecasting public expenditure on health care has been based on a six-step cohort method. The results have indicated that the cost of updating the age structure of Ukraine’s population every year will decrease due to the aging of the population, and the overall impact of demographic processes will be negative. The impact of mass migration due to the war creates a significant change in health care costs, requiring administrative bodies to monitor the situation promptly and make appropriate changes to the structure of budget expenditure.