Ultrashort and intense extreme ultraviolet (XUV) and X-ray pulses readily available at free-electron lasers (FELs) enable studying non-linear light−matter interactions on femtosecond timescales. Here, we report on the non-linear fluence dependence of magnetic scattering of Co/Pt multilayers, using FERMI FEL’s 70-fs-long single and double XUV pulses, the latter with a temporal separation of 200 fs, with a photon energy slightly detuned to the Co M2,3 absorption edge. We observe a quenching in magnetic scattering that sets-in already in the non-destructive fluence regime of a few mJ/cm² typically used for FEL-probe experiments on magnetic materials. Calculations of the transient electronic structure in tandem with a phenomenological modeling of the experimental data by means of ultrafast demagnetization unambiguously show that XUV-radiation-induced demagnetization is the dominant mechanism for the quenching in the investigated fluence regime of <50 mJ/cm², while light-induced changes of the electronic core levels are predicted to additionally occur at higher fluences. The modeling of the data further indicates that the demagnetization proceeds on the sub-20-fs timescale. This ultrashort timescale is consistent with non-coherent models for ultrafast demagnetization, considering the sub-femtosecond lifetime of hot electrons with energies of a few 10 eV generated by the XUV radiation.