We have studied the effect of a random superconducting order parameter on the localization of quasiparticles, by numerical finite-size scaling of the Bogoliubov-de Gennes tight-binding Hamiltonian. Anderson localization is obtained in d = 2 and a mobility edge where the states localize is observed in d = 3. The critical behavior and localization exponent are universal within error bars both for real and complex random order parameter. Experimentally these results imply a suppression of thr electronic contribution to thermal transport from states above the bulk energy gap.