Electron spin resonance measurements in EuFe2As2 single crystals revealed an absorption spectrum of a single resonance with Dysonian lineshape. Above the spin-density wave transition at TSDW = 190 K the spectra are isotropic and the spin relaxation is strongly coupled to the CEs resulting in a Korringa-like increase of the linewidth. Below TSDW, a distinct anisotropy develops and the relaxation behavior of the Eu spins changes drastically into one with characteristic properties of a magnetic insulating system, where dipolar and crystal-field interactions dominate. This indicates a spatial confinement of the CEs to the FeAs layers in the SDW state.