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Motivated by their utility in CdTe-based thin film photovoltaics (PV) devices, an investigation of thin films of the magnesium-zinc oxide (MgxZn1−xO or MZO) alloy system was undertaken applying spectroscopic ellipsometry (SE). Dominant wurtzite phase MZO thin films with Mg contents in the range 0 ≤ x ≤ 0.42 were deposited on room temperature soda lime glass (SLG) substrates by magnetron co-sputtering of MgO and ZnO targets followed by annealing. The complex dielectric functions ε of these films were determined and parameterized over the photon energy range from 0.73 to 6.5 eV using an analytical model consisting of two critical point (CP) oscillators. The CP parameters in this model are expressed as polynomial functions of the best fitting lowest CP energy or bandgap E0 = Eg, which in turn is a quadratic function of x. As functions of x, both the lowest energy CP broadening and the Urbach parameter show minima for x ~ 0.3, which corresponds to a bandgap of 3.65 eV. As a result, it is concluded that for this composition and bandgap, the MZO exhibits either a minimum concentration of defects in the bulk of the crystallites or a maximum in the grain size, an observation consistent with measured X-ray diffraction line broadenings. The parametric expression for ε developed here is expected to be useful in future mapping and through-the-glass SE analyses of partial and complete PV device structures incorporating MZO.