Glaciers calving icebergs into the ocean significantly contribute to sea-level rise and can trigger tsunamis, posing severe hazards for coastal regions. Computational modeling of such multiphase processes is a great challenge involving complex solid–fluid interactions. Here, a new continuum damage Material Point Method has been developed to model dynamic glacier fracture under the combined effects of gravity and buoyancy, as well as the subsequent propagation of tsunami-like waves induced by released icebergs. We reproduce the main features of tsunamis obtained in laboratory experiments as well as calving characteristics, the iceberg size, tsunami amplitude and wave speed measured at Eqip Sermia, an ocean-terminating outlet glacier of the Greenland ice sheet. Our hybrid approach constitutes important progress towards the modeling of solid–fluid interactions, and has the potential to contribute to refining empirical calving laws used in large-scale earth-system models as well as to improve hazard assessments and mitigation measures in coastal regions, which is essential in the context of climate change.