The magnetocaloric effect (MCE) in paramagnetic materials has been widely used for attaining very low temperatures by applying a magnetic field isothermally and removing it adiabatically. The effect can be exploited also for room temperature refrigeration by using recently discovered giant MCE materials. In this letter, we report on an inverse situation in Ni-Mn-Sn alloys, whereby applying a magnetic field adiabatically, rather than removing it, causes the sample to cool. This has been known to occur in some intermetallic compounds, for which a moderate entropy increase can be induced when a field is applied, thus giving rise to an inverse magnetocaloric effect. However, the entropy change found for some ferromagnetic Ni-Mn-Sn alloys is just as large as that reported for giant MCE materials, but with opposite sign. The giant inverse MCE has its origin in a martensitic phase transformation that modifies the magnetic exchange interactions due to the change in the lattice parameters.