We evaluated the irradiation damage induced by hard X-ray free-electron lasers to platinum/carbon multilayers intended for use in a focusing reflective mirror. In order to determine the damage threshold, we compared X-ray reflectivities before and after irradiation at the first-order Bragg angle using a focused X-ray free-electron laser with a beam size of approximately 1 μm and a pulse energy ranging from 0.01 to 10 μJ at a photon energy of 10 keV. We confirmed that the damage threshold of the platinum/carbon multilayer with a bilayer period of 3 nm was 0.051 μJ/μm(2), which is sufficiently higher than that in practical applications.