I will argue that if dark matter is produced via processes with finite correlation length in the early universe, then there is a lower bound on the mass of dark matter particles (m > 10^(-19) eV). For such dark matter, there is both (i) a free streaming suppression and (ii) white-noise enhancement in the dark matter density power spectrum. The absence of these in the existing observational data (for example, Ly-a) provides a bound on the mass. This relatively model-independent bound will improve rapidly as observations probe dark matter at even smaller length scales. The bound can also be made stronger by many orders of magnitude if additional model-dependent assumptions are included.