Results of radiation tests of Hamamatsu 2.0 x 2.0~mm2 through-silicon-via (S13360-2050VE) multi-pixel photon counters, or MPPCs [1], are presented. Distinct sets of eight MPPCs were exposed to four different 1~MeV neutron equivalent doses of 200 MeV protons. Measurements of the breakdown voltage, gain and noise rates at different bias overvoltages, photoelectron thresholds, and LED illumination levels were taken before and after irradiation. No significant deterioration in performance was observed for breakdown voltage, gain, and response. Noise rates increased significantly with irradiation. These studies were undertaken in the context of MPPC requirements for the Cosmic Ray Veto detector of the Mu2e experiment at the Fermi National Accelerator Laboratory.