Fornal and Grinstein recently proposed that the discrepancy between two different methods of neutron lifetime measurements, the beam and bottle methods, can be explained by a previously unobserved dark matter decay mode, n→X+γ. We perform a search for this decay mode over the allowed range of energies of the monoenergetic γ ray for X to be dark matter. A Compton-suppressed high-purity germanium detector is used to identify γ rays from neutron decay in a nickel-phosphorous-coated stainless-steel bottle. A combination of Monte Carlo and radioactive source calibrations is used to determine the absolute efficiency for detecting γ rays arising from the dark matter decay mode. We exclude the possibility of a sufficiently strong branch to explain the lifetime discrepancy with 97% confidence.