Motivated by experimental indications of a significant presence of heavy nuclei in the cosmic ray flux at ultra high energies (greater than or similar to 10(19) eV), we consider the effects of Planck scale suppressed Lorentz Invariance Violation (LIV) on the propagation of cosmic ray nuclei. In particular we focus on LIV effects on the photodisintegration of nuclei onto the background radiation fields. After a general discussion of the behavior of the relevant quantities, we apply our formalism to a simplified model where the LIV parameters of the various nuclei are assumed to kinematically result from a single LIV parameter for the constituent nucleons, eta, and we derive constraints on eta. Assuming a nucleus of a particular species to be actually present at 10(20) eV the following constraints can be placed: -3 x 10(-2) less than or similar to eta less than or similar to 4 for Fe-56, -2 x 10(-3) less than or similar to eta less than or similar to 3 x 10(-2) for O-16 and -7 x 10(-5) less than or similar to eta less than or similar to 1 x 10(-4) for He-4, respectively.