We have investigated the electronic structure and optical properties of zinc molybdenum oxide (Zn$_2$Mo$_3$O$_8$) by using both first-principle calculations and experiments. Optical properties of this material is very similar to other ternary oxides of tetravalent molybdenum (A$_2$Mo$_3$O$_8$: A = Mg, Fe, Cd); therefore, this study provides meaningful insight into optical properties and possible phtotovoltaic applicability of these class of metal oxide cluster compounds. We use state-of-the-art methods, based on density functional theory and the GW approximation to the self-energy, to obtain the quasiparticle band structure and absorption spectra of the material. Our calculations shows that Zn$_2$Mo$_3$O$_8$ is a near indirect gap semiconductor with an indirect gap of 3.14 eV. The direct gap of the material is 3.16 eV. We also calculate the optical absorption in the material. Calculated results compare well with UV–visible spectroscopy and spectroscopic ellipsometry measurements done on polycrystalline thin films of Zn$_2$Mo$_3$O$_8$. We show the material has a large excitonic binding energy of 0.78 eV.