Submarine melting is one of the major mechanisms of ice loss from marine-terminating glaciers and ice shelves, but its contribution is yet to be fully understood. Here, we demonstrate the feasibility of monitoring melting using passive underwater acoustics, by sensing the loud crackling sound produced during melting due to the release of pressurised ice-trapped bubbles. We profile the acoustic field in glacial bays in Svalbard using a hydrophone array, and show that the sound level in the bay contains clues on the melt activity. The sound level's interpretation is hindered by its spatial variability, which we suppress using a model of melt-induced acoustic activity. Thereby, we show that the sound generated at the glacier terminus is correlated with the ablation rate at the calving glacier front and the water temperature, and thus linked to the melt rate. This marks a step forward in using passive acoustics to monitor submarine melt, paving the way for an autonomous, long-term, large-scale monitoring tool providing data that can inform assessments and simulations of ice sheet loss and sea level rise.