Electron paramagnetic resonance spectroscopy is used to investigate the thermal stability of the Aluminum–Zinc vacancy (AlZn–VZn) complex created in bulk single crystalline ZnO by room temperature electron irradiation with an energy of 1.2 MeV. Two different stages in the annealing process at 160 and 250 °C with apparent activation energies of EA1 = 1.5 ± 0.2 eV and EA2 = 1.9 ± 0.2 eV, respectively, are observed. The second stage leads to the complete annealing out of the (AlZn–VZn) complex and is accompanied by restoration of the concentration of the AlZn shallow donor centers to its initial value in as-grown (i.e., not irradiated) material. The obtained results prove that the (AlZn–VZn) complex is the dominant acceptor responsible for compensation of n-type-dopants in the studied Al-containing ZnO samples.