Weak-scale dark matter particles, in collisions with nuclei, can mediate transitions between different nuclear energy levels. In particular, owing to sizeable momentum exchange, dark matter particles can enable de-excitation of nuclear isomers that are extremely long lived with respect to regular radioactive decays. In this Letter, we utilize data from a past experiment with ^{180}Ta^{m} to search for γ lines that would accompany dark matter induced de-excitation of this isomer. Nonobservation of such transitions above background yields the first direct constraint on the lifetime of ^{180}Ta^{m} against dark matter initiated transitions: T_{1/2}>1.3×10^{14} a at 90% credibility. Using this result, we derive novel constraints on dark matter models with strongly interacting relics and on models with inelastic dark matter particles. Existing constraints are strengthened by this independent new method. The obtained limits are also valid for the standard model γ-decay of ^{180}Ta^{m}.