Abstract At the low temperature and high density conditions of a neutron star crust neutrons are degenerate. In this work, we study the effect of this degeneracy on the capture rates of neutrons on neutron rich nuclei in accreted crusts. We use a statistical Hauser-Feshbach model to calculate neutron capture rates and find that neutron degeneracy can increase rates significantly. Changes increase from a factor of a few to many orders of magnitude near the neutron drip line. We also quantify uncertainties due to model inputs for masses, γ-strength functions, and level densities. We find that uncertainties increase dramatically away from stability and that degeneracy tends to increase these uncertainties further, except for cases near the neutron drip line where degeneracy leads to more robustness. As in the case of capture of classically distributed neutrons, variations in the mass model have the strongest impact. To ease the incorporation of neutron degeneracy in nucleosynthesis networks, we provide tabulated results of capture rates as well as fits as function of temperature and neutron chemical potential using an approximation with significantly improved accuracy.