Models for light dark matter particles with masses below 1 GeV/c Formula omitted are a natural and well-motivated alternative to so-far unobserved weakly interacting massive particles. Gram-scale cryogenic calorimeters provide the required detector performance to detect these particles and extend the direct dark matter search program of CRESST. A prototype 0.5 g sapphire detector developed for the Formula omitted-cleus experiment has achieved an energy threshold of Formula omitted eV. This is one order of magnitude lower than for previous devices and independent of the type of particle interaction. The result presented here is obtained in a setup above ground without significant shielding against ambient and cosmogenic radiation. Although operated in a high-background environment, the detector probes a new range of light-mass dark matter particles previously not accessible by direct searches. We report the first limit on the spin-independent dark matter particle-nucleon cross section for masses between 140 and 500 MeV/c Formula omitted.