Core-shell isomers of small magnesium clusters "doped" with a hydrogen molecule are theoretically studied and predicted to be weakly stable or metastable for different sizes of the system, allowing a low-temperature release of hydrogen. Evolution of H(2) inside Mg(n) is followed from the molecular species to two H atoms. Among properties analyzed are equilibrium geometries, dissociation energies, charge distributions, vertical energies of electronic excitation, ionization and electron attachment, and vibrational frequencies.