57Fe transmission and conversion electron Mössbauer spectroscopy as well as XRD were used to study the effect of swift heavy ion irradiation on stress-annealed FINEMET samples with a composition of Fe73.5Si13.5Nb3B9Cu1. The XRD of the samples indicated changes neither in the crystal structure nor in the texture of irradiated ribbons as compared to those of non-irradiated ones. However, changes in the magnetic anisotropy both in the bulk as well as at the surface of the FINEMET alloy ribbons irradiated by 160 MeV 132Xe ions with a fluence of 1013 ion cm−2 were revealed via the decrease in relative areas of the second and fifth lines of the magnetic sextets in the corresponding Mössbauer spectra. The irradiation-induced change in the magnetic anisotropy in the bulk was found to be similar or somewhat higher than that at the surface. The results are discussed in terms of the defects produced by irradiation and corresponding changes in the orientation of spins depending on the direction of the stress generated around these defects.