Hybrid organic–inorganic perovskites combine outstanding optoelectronic properties with low-cost fabrication, yet their structural fragility under environmental factors limits device stability. In this context, the use of pressure offers the enticing possibility of unveiling the microscopic mechanisms behind structural changes and the eventual collapse or decomposition of the material. In this work, we have employed high-resolution inelastic neutron scattering in the gigapascal regime alongside first-principles calculations to probe the pressure–temperature phase behavior of methylammonium lead iodide (MAPbI3). Below 1 GPa and 150 K, pressurization leads to a stiffening of spectral features sensitive to NH···I hydrogen-bonding motifs, concomitant with a contraction of the inorganic framework. Between 1 and 1.25 GPa at these low temperatures, the INS data undergo a pronounced broadening, corresponding to the formation of an orientational glass of organic cations whose immediate environment is encapsulated by a corner-sharing metal-halide framework.