We propose a search for low mass dark matter particles through momentum recoils caused by their scattering from trapped, nanometer-scale objects. Our projections show that even with a modest array of femtogram-mass sensors, parameter space beyond the reach of existing experiments can be explored. The case of smaller, attogram-mass sensors is also analyzed-where dark matter can coherently scatter from the entire sensor-enabling a large enhancement in the scattering cross-section relative to interactions with single nuclei. Large arrays of such sensors have the potential to investigate new parameter space down to dark matter masses as low as 10 keV. If recoils from dark matter are detected by such sensors, their inherent directional sensitivity would allow an unambiguous identification of a dark matter signal.