Studies of the seasonal and annual patterns of glacier velocities improve our understanding of the ice volume, topography, responses to climate change, and surge events of glaciers. Such studies are especially relevant and equally rare for the Himalayan glaciers, which supply many rivers that sustain some of the most heavily populated mountainous regions in the world. In particular, the control of the hypsometric distribution of geomorphometric parameters, such as slope, aspect, and curvature, on the dynamics of Himalayan glaciers have never been studied so far, at the river basin scale. Here, we present the degree to which topographic and hypsometric parameters affect the seasonal and annual average flow velocities of 112 glaciers in the Baspa River basin in the Western Indian Himalaya by analysing Global Land Ice Velocity Extraction from Landsat 8 (GoLIVE) datasets for the years 2013–2017. We observe, (i) significant heterogeneity in topographic controls on the velocities of these glaciers, (ii) elevation and the seasons play important roles in regulating the degree to which morphometric parameters (slope, aspect, and curvature) affect these velocities, (iii) a possible polythermal regime promoting both sliding and deformational forms of motion in a majority of these glaciers, and (iv) a detailed analysis of complex topographic controls within various elevation zones using a novel hypso-morphometric approach. These findings can help us to better model the dynamics of Himalayan glaciers and their responses to the future climatic scenarios. The inferences also suggest the need to incorporate dynamic topography in glacio-hydrological models in the wake of constant glacial evolutions.