Single crystals of Ba 1−x Eu x Fe 2 As 2 were studied by magnetic susceptibility, heat capacity, resistivity, and electron spin resonance (ESR) measurements. Spin-density wave (at T SDW ) and antiferromagnetic (at T N ) phase transitions were mapped as a function of x. For x 0.2, we found a single Eu 2+ ESR Dysonian line that presents an isotropic linear increase (Korringa) of its linewidth ( H ) above T SDW which systematically decreases with decreasing x. In contrast, for a critical concentration x c (0.10 < x c < 0.20), H decreases with increasing T , suggesting a distinct relaxation process that we associate with a Eu 2+ Kondo single impurity regime. The Korringa rate suppression towards the Ba-rich compounds is claimed to be due to the reduction of the q-dependent exchange interaction between the Eu 2+ f electrons and the conduction electrons, which is likely associated with an increasing of localization of Fe d electrons. This result may help the understanding of the SDW phase suppression (that can lead to superconductivity) in this class of materials.