Phenological responses to climate change frequently vary among trophic levels, which can result in increasing asynchrony between the peak energy requirements of consumers and the availability of resources. Migratory birds use multiple habitats with seasonal food resources along migration flyways. Spatially heterogeneous climate change could cause the phenology of food availability along the migration flyway to become desynchronized. Such heterogeneous shifts in food phenology could pose a challenge to migratory birds by reducing their opportunity for food availability along the migration path and consequently influencing their survival and reproduction. We develop a novel graph-based approach to quantify this problem and deploy it to evaluate the condition of the heterogeneous shifts in vegetation phenology for 16 migratory herbivorous waterfowl species in Asia. We show that climate change-induced heterogeneous shifts in vegetation phenology could cause a 12% loss of migration network integrity on average across all study species. Species that winter at relatively lower latitudes are subjected to a higher loss of integrity in their migration network. These findings highlight the susceptibility of migratory species to climate change. Our proposed methodological framework could be applied to migratory species in general to yield an accurate assessment of the exposure under climate change and help to identify actions for biodiversity conservation in the face of climate-related risks.