Continuous-wave, time-integrated, and time-resolved photoluminescence experiments are used to study the excitonic optical recombinations in wurtzite ZnO/Zn0.78Mg0.22O quantum wells of varying widths. By comparing experimental results with a variational calculation of excitonic energies and oscillator strengths, we determine the magnitude (0.9 MV/cm) of the longitudinal electric field that is induced by both spontaneous and piezoelectric polarizations. The quantum-confined Stark effect counteracts quantum confinement effects for well widths larger than 3 nm, leading to emission energies that can lie 0.5 eV below the ZnO excitonic gap and to radiative lifetimes that can be larger than milliseconds.