Photons of energy larger than 100 MeV from long GRBs arrive a few seconds after <10 MeV photons do. We show that this delay is a natural consequence of a magnetic-dominated relativistic jet. The much slower acceleration of a magnetic jet with radius (compared with a hot baryonic outflow) results in high-energy γ-ray photons to be converted to electron–positron pairs out to a larger radius, whereas lower energy γ-rays of energy less than ∼10 MeV can escape when the jet crosses the Thomson photosphere. The resulting delay for the arrival of high-energy photons is found to be similar to the value observed by the Fermi satellite for a number of GRBs. A prediction of this model is that the delay should increase with photon energy (E) as ∼E0.17 for E > 100 MeV. The delay depends almost linearly on burst redshift, and on the distance from the central compact object where the jet is launched (R0). Therefore, the delay in arrival of >102 MeV photons can be used to estimate burst redshift if the magnetic jet model for γ-ray generation is correct and R0 is roughly the same for long GRBs.