Hydrothermal alteration may weaken volcanic rocks, causing the gravitational instability of portions of active volcanoes with potentially hazardous collapses. Here we show high-resolution multibeam, magnetic and gravity surveys of the Marsili seamount, the largest active volcano of Europe located in the southern Tyrrhenian back-arc basin. These surveys reveal zones with exceptionally low densities and with vanishing magnetizations, due probably to the comminution of basalts during hyaloclastic submarine eruptions and to their post-eruptive hydrothermal alteration. The location of these regions correlates with morphological data showing the occurrence of past collapses. Similar evidence has been obtained from pre-existing data at Vavilov Seamount, another older volcanic system in the Tyrrhenian back-arc basin. Here a large volume of at least 50 km3 may have collapsed in a single event from its 40 km long western flank. Given the similarities between these volcanoes, a large collapse event may also be expected at Marsili.