Recently, deuterium-labeled drugs, such as deutetrabenazine, have attracted considerable attention. Consequently, understanding the reaction mechanisms of deuterium-labeled drugs is crucial, both fundamentally and for real applications. To understand the mechanisms of H- and D-transfer reactions, in this study, we used deuterated anisole as a deutetrabenazine model and computationally considered the nuclear quantum effects of protons, deuterons, and electrons. We demonstrated that geometrical differences exist in the partially and fully deuterated methoxy groups and hydrogen-bonded structures of intermediates and transition states due to the H/D isotope effect. The observed geometrical features and electronic structures are ascribable to the different nuclear quantum effects of protons and deuterons. Primary and secondary kinetic isotope effects (KIEs) were calculated for H- and D-transfer reactions from deuterated and undeuterated anisole, with the calculated primary KIEs in good agreement with the corresponding experimental data. These results reveal that the nuclear quantum effects of protons and deuterons need to be considered when analyzing the reaction mechanisms of H- and D-transfer reactions and that a theoretical approach that directly includes nuclear quantum effects is a powerful tool for the analysis of H/D isotope effects in H- and D-transfer reactions.