The effects of pressure on the structure of ice XI-an ordered form of the phase of ice Ih, which is known to amorphize under pressure-are investigated theoretically using density-functional theory. We find that pressure induces a mechanical instability, which is initiated by the softening of an acoustic phonon occurring at an incommensurate wavelength, followed by the collapse of the entire acoustic band and by the violation of the Born stability criteria. It is argued that phonon collapse may be a quite general feature of pressure-induced amorphization. The implications of our findings for the amorphization of ice Ih are also discussed.