We have studied the damage in ferrimagnetic yttrium iron garnet, Y3Fe5O12 or YIG, produced by energetic heavy ion bombardment, for which the electronic stopping power is much higher than the nuclear stopping power. Epitaxial thin films of YIG on (111)-Gd3Ga5O12 substrates were thus irradiated at room temperature with 50 MeV 32S, 50 MeV 63Cu, 235 MeV 84Kr, and with 59 MeV, 185 MeV and 792 MeV 132Xe ion beams. The film thicknesses were always smaller than the ion mean projected ranges, in order to avoid implantation effects in the layers. The resulting damage was then studied by high resolution X-ray diffraction, channeling Rutherford backscattering (RBS) spectroscopy and room temperature magnetization measurements.After these ion irradiations, the structural as well as the ferrimagnetic long-range orders are progressively destroyed. X-ray measurements on 84Kr irradiated samples show the presence of compressive lateral macrostresses in the films due to the coexistence of crystalline and disordered phases. These stresses are partly relaxed away at high fluences, when the amount of disordered phase is high enough (around 45%).Cross section data for this damage process are deduced from the RBS and 300 K saturation magnetization measurements for six different values of the electronic energy loss, between 7 and 27 MeVμm−1. The damage cross section increases nonlinearly as a function of the electronic stopping power, then seems to level off above 22 MeV μm −1. However the comparison with previous works indicates that the electronic stopping power might not be the only key-parameter in this process, where the ion beam energy parameters might play some role.