The adsorption and dissociation of hydrogen on Zn-exchanged zeolites has been studied theoretically by density functional theory (DFT). Diverse types of active sites have been employed for the Zn cation, such as: placed on different rings (4T and 5T), in the (ZnO)4 (in a cubic configuration cluster) and in the [Zn–O–Zn]2+ dimer complex. The Zn(II) cation is most exposed to probe molecules when situated on 4T ring of zeolites. In this position, the cation activates the infrared stretching band of the hydrogen molecule, which is not observed when Zn(II) sits on 5T rings. The assignment of the band shifts found in the experimental IR spectra of hydrogen adsorption, which were associated to the cation position in the zeolite framework, had to be revised following the results for the calculated shifts. Larger shifts are associated to the cationic position at small rings. In the case for (ZnO)4 the dissociative adsorption is more favorable. The calculated activation energy is the lowest among all sites studied. The results have also confirmed the current proposal that ZnO microparticles are responsible for the large H–H stretching shift and the H2 dissociation on Zn(II) sites in zeolites.