We provide a scenario where naturally small and calculable neutrino masses arise from a supersymmetry-breaking renormalization-group-induced vacuum expectation value. The construction consists of an extended version of the next-to-minimal supersymmetric standard model and the mechanism is illustrated for a universal choice of the soft supersymmetry-breaking parameters. The lightest supersymmetric particle can be an isosinglet scalar neutrino state, potentially viable as WIMP dark matter through its Higgs new boson coupling. The scenario leads to a plethora of new phenomenological implications at accelerators including the Large Hadron Collider. © 2010 The American Physical Society.