Proliferative kidney disease (PKD) affects freshwater salmonid populations in temperate European and North-American rivers. It is caused by the endoparasitic myxozoan Tetracapsuloides bryosalmonae, which exploits freshwater bryozoans as intermediate hosts. Incidence and fish mortality are enhanced by warmer water temperatures. Therefore, environmental change is feared to increase the severity of PKD outbreaks and extend the disease range to higher latitude and altitude regions. Building on a recently developed local model of PKD transmission, a spatially-explicit metacommunity framework is developed to study the spatial effects in the spread of the disease in idealized stream networks. At the local community scale, the model accounts for demographic and epidemiological dynamics of bryozoans and fish. At the network scale, the model couples the dynamics of each community through hydrological transport of parasite spores and fish mobility. The model also explicitly accounts for how habitat characteristics and hydrological conditions change along a river network. The model is applied to synthetic river network replicas derived from Optimal Channel Networks (OCNs), spanning trees known to reproduce all mutually connected scaling exponents of topological and metric features of real rivers. Stability analysis of the local model shows that the introduction of the parasite in a disease-free community is likely to trigger a disease outbreak. Moreover, we show how network connectivity and hydrological conditions critically control the spatial distribution of the prevalence of PKD and the celerity of invasion fronts in the upstream and downstream directions. The developed mathematical model helps further our understanding of the drivers of fish distribution in riverine ecosystems and provide the basis for the development of possible intervention and management tools.