Ferroelectric materials possess a spontaneous electric polarization and may be utilized in various technological applications ranging from nonvolatile memories to solar cells and light polarizers. Recently, hexagonal rare-earth manganites, h-RMnO3 (R is a rare-earth ion), have attracted considerable interest due to their intricate multiferroic properties and improper ferroelectricity characterized by a sizable remnant polarization and high Curie temperature. Here we demonstrate that these compounds can serve as very efficient photovoltaic materials and, in addition, possess remarkable optical anisotropy properties. Using first-principles methods based on density functional theory and considering h-TbMnO3 as a representative manganite, we predict a strong light absorption of this material in the solar spectrum range, resulting in a maximum light-to-electricity energy conversion efficiency of up to 33%. We also predict an extraordinary optical linear dichroism and linear birefringence properties of h-TbMnO3 in a broad range of optical frequencies. These results uncover the unexplored potential of hexagonal rare-earth manganites to serve as photovoltaics in solar cells and as absorptive and birefringent light polarizers.