Edited because I can't read.
The Greisen–Zatsepin–Kuzmin (GZK) limit is one particular theoretical limit involving high-energy protons. Beyond this energy limit, protons scatter too much with the cosmic microwave background radiation to travel any significant distance towards Earth.
Now, in principle, photons should also interact with the CMB, scattering of two photons has already been experimentally confirmed. There are reference frames in which CMB photons have (nearly) arbitrarily high energies, and so one would expect pair production from extremely high energy gamma rays. According to this source the threshold energy is about $10^{15}\,\mathrm{eV}$.