Time-resolved photoluminescence spectroscopy (TRPL) has been employed to study a set of ZnO/Zn1-xMgxO (x = 0.12) multiple quantum wells (MQWs) grown by laser molecular beam epitaxy, with well-width L-w varying from 6.91 to 46.5 Angstrom. We have estimated the L-w dependence of radiative and nonradiative recombination lifetimes of excitons at low temperature (5 K). Radiative recombination lifetimes were dramatically increased at narrow L-w and the thermal release effect of excitonic localization is discussed. On the other hand, the nonradiative recombination rates were almost constant over the L-w range studied, so we conclude that suppression of quantum efficiency due to carrier leakage can be avoided even at narrow L-w.