Abstract: The current study presents a composite material based on magnesium hydride with the addition of aluminum, obtained by the method of electrical explosion of wires (EEW). The study demonstrated that the material has improved hydrogen interaction characteristics, which is associated with its core–shell structure, defect formation during milling, and the hydrogenation process. The combination of these factors contributes to a decrease in the activation energy of desorption from (161 ± 2) to (109 ± 1) kJ/mol, and consequently, to a reduction in operating temperatures. The data obtained are correlate with a model in which mechanochemical treatment and the formation of Mg–Al interfaces induce a developed network of vacancies, dislocations, and increased microstrains. Based on all of the above, a corresponding mechanism for low-temperature hydrogen desorption from the composite was described.