Using a nano-scale grid as a phase-shifting component, an atom interferometer has been utilized to study atom-surface van der Waals (VdW) interactions. We report phase shifts on the order of 0.2 rad, with a few percent uncertainty. We also report the velocity-dependent attenuation of atomic de Broglie wave amplitude that occurs in conjunction with the observed phase shifts. From these data we deduce the strength of the VdW potential and its dependence on the atom-surface separation. We discuss how our measurements can be used to set limits on the strength of non-Newtonian gravity at short length scales and we discuss the possibility of measuring the atom-surface interactions over a larger range of atom-surface distances. We also compare our results to several theoretical predictions for the VdW potential of Li near a variety of surfaces.