Records of Alpine microseismicity are a powerful tool to study landscape-shaping processes and warn against hazardous mass movements. Unfortunately, seismic sensor coverage in Alpine regions is typically insufficient. Here we show that distributed acoustic sensing (DAS) bridges critical observational gaps of seismogenic processes in Alpine terrain. Dynamic strain measurements in a 1 km long fiber optic cable on a glacier surface produce high-quality seismograms related to glacier flow and nearby rock falls. The nearly 500 cable channels precisely locate a series of glacier stick-slip events (within 20-40 m) and reveal seismic phases from which thickness and material properties of the glacier and its bed can be derived. As seismic measurements can be acquired with fiber optic cables that are easy to transport, install and couple to the ground, our study demonstrates the potential of DAS technology for seismic monitoring of glacier dynamics and natural hazards.