Neutron stars are used to set constraints on the characteristics of weakly interacting massive particles (WIMP's) suggested as dark-matter candidates. Some special classes of WIMP's are ruled out because they would be trapped in neutron stars, concentrate towards the star center, and become self-gravitating. This results in the formation of a mini black hole that consumes the neutron star, transforming it into a black hole, on a time scale shorter than observed ages of neutron stars in various astrophysical systems.