Repeating long-period (lp) earthquakes are commonly observed in volcanic regions worldwide. They are usually explained in terms of a volcanic source effect or anomalous propagation through the volcano. Recently, large lp events have also been associated with the motion of massive ice streams. Our joint analysis of climatic and new seismic data shows that small lp events observed at Katla volcano, Iceland, are in fact related to ice movement in a steep outlet glacier and not, as previously thought, to volcanic intrusive activity. The over 13000 lp events recorded since 2000 are consistent in character and magnitude with seasonal changes of the glacier. As the current global warming trend could cause similar earthquake sequences at other glacier covered volcanoes, identifying them as glacial rather than eruption precursors is vital.