We report the effect of hydrostatic pressure on the magnetic and structural properties of the shape-memory Heusler alloy Ni50Mn35In15. Magnetization and x-ray diffraction experiments were performed at hydrostatic pressures up to 5 GPa using diamond anvil cells. Pressure stabilizes the martensitic phase, shifting the martensitic transition to higher temperatures and suppresses the ferromagnetic austenitic phase. Above ~3 GPa, where the martensitic-transition temperature approaches the Curie temperature in the austenite, the magnetization shows no indication of ferromagnetic ordering anymore. We further find an extremely large temperatureregion with a mixture of martensite and austenite phases, which directly relates to the magnetic properties.