One of the most unique and robust experimental facts about iron-based superconductors is the renormalization of the electronic band dispersion by factor of 3 and more near the Fermi level. Obviously related to the electron pairing, this prominent deviation from the band theory lacks understanding. Experimentally studying the entire spectrum of the valence electrons in iron arsenides, we have found an unexpected depletion of the spectral weight in the middle of the iron-derived band, which is accompanied by a drastic increase of the scattering rate. At the same time, the measured arsenic-derived band exhibits very good agreement with theoretical calculations. We show that the low-energy Fermi velocity renormalization should be viewed as a part of the modification of the spectral function by a strong electronic interaction. Such an interaction with an energy scale of the whole d band appears to be a hallmark of many families of unconventional superconductors.