We report the effect of the atomic mass of the sputtering gas (He, Ne, Ar, Kr, and Xe) on the structure and optical properties of nanocrystalline cuprous oxide (Cu2O) thin films deposited by dc magnetron sputtering. The crystal structure and surface morphology were studied by X-ray diffraction (XRD) and atomic force microscopy (AFM) respectively. We find that the atomic mass of the sputtering gas significantly affects the primary crystallite size as well as the surface morphology and texture. Optical reflectance and transmission measurements show that the nanocrystalline thin films are transparent over most of the visible region. The HOMO-LUMO gap obtained from optical absorption spectra show a size-dependent quantum shift with respect to the bulk band gap reported for Cu2O (2.1 eV).