The excitonic properties of high-quality ZnO/Zn0.88Mg0.12O multiquantum wells grown by laser-molecular-beam epitaxy were investigated using temperature-dependent optical absorption spectra from 5 K to room temperature. The strength of exciton-longitudinal-optical (LO) -phonon coupling was deduced from the temperature dependence of the linewidth of the fundamental excitonic peak. Effective reduction of the exciton-LO-phonon coupling with decreasing the well width was observed, which is consistent with the confinement-induced enhancement of the exciton binding energy. The thermal shift of the lowest excitonic energy is independent of well width, indicating that the strain effect is negligible for this material.