We have performed an angle-resolved photoemission spectroscopy study of the new superconductor Ba0.6K0.4Fe2As2 in the low energy range. We report the observation of an anomaly around 25 meV in the dispersion of superconducting Ba0.6K0.4Fe2As2 samples that nearly vanishes above T_{c}. The energy scale of the related mode (13+/-2 meV) and its strong dependence on orbital and temperature indicates that it is unlikely related to phonons. Moreover, the momentum locations of the kink can be connected by the antiferromagnetic wave vector. Our results point towards an unconventional electronic origin of the mode and the superconducting pairing in the Fe-based superconductors, and strongly support the antiphase s-wave pairing symmetry.