AbstractRock glaciers in semiarid mountains contain large amounts of ice and might be important water stores aside from glaciers, lakes, and rivers. Yet whether and how rock glaciers interact with river channels in mountain valleys remains largely unresolved. We examine the potential for rock glaciers to block or disrupt river channels, using a new inventory of more than 2000 intact rock glaciers that we mapped from remotely sensed imagery in the Karakoram (KR), Tien Shan (TS), and Altai (ALT) mountains. We find that between 5% and 14% of the rock glaciers partly buried, blocked, diverted or constricted at least 95 km of mountain rivers in the entire study area. We use a Bayesian robust logistic regression with multiple topographic and climatic inputs to discern those rock glaciers disrupting mountain rivers from those with no obvious impacts. We identify elevation and potential incoming solar radiation (PISR), together with the size of feeder basins, as dominant predictors, so that lower‐lying and larger rock glaciers from larger basins are more likely to disrupt river channels. Given that elevation and PISR are key inputs for modelling the regional distribution of mountain permafrost from the positions of rock‐glacier toes, we infer that river‐blocking rock glaciers may be diagnostic of non‐equilibrated permafrost. Principal component analysis adds temperature evenness and wet‐season precipitation to the controls that characterise rock glaciers impacting on rivers. Depending on the choice of predictors, the accuracy of our classification is moderate to good with median posterior area‐under‐the‐curve values of 0.71–0.89. Clarifying whether rapidly advancing rock glaciers can physically impound rivers, or fortify existing dams instead, deserves future field investigation. We suspect that rock‐glacier dams are conspicuous features that have a polygenetic history and encourage more research on the geomorphic coupling between permafrost lobes, river channels, and the sediment cascades of semiarid mountain belts. © 2018 John Wiley & Sons, Ltd.