A rigorous treatment of the uncertainty in the underlying nuclear data on silicon displacement damage metrics is presented. The uncertainty in the cross sections and recoil atom spectra are propagated into the energy-dependent uncertainty contribution in the silicon displacement kerma and damage energy using a Total Monte Carlo treatment. An energy-dependent covariance matrix is used to characterize the resulting uncertainty. A strong correlation between different reaction channels is observed in the high energy neutron contributions to the displacement damage metrics which supports the necessity of using a Monte Carlo based method to address the nonlinear nature of the uncertainty propagation.