© 2020 IOP Publishing Ltd. The magnetic susceptibility of the 1/1 approximants to icosahedral quasicrystals in a series of Cd85-x Mg x Tb15 (x = 5, 10, 15, 20) alloys was investigated in detail. The occurrence of antiferromagnetic (AFM) to spin-glass (SG)-like transition was noticed by increasing Mg. Transmission electron microscopy analysis evidenced a correlation between the magnetic transition and suppression of the monoclinic superlattice ordering with respect to the orientation of the Cd4 tetrahedron at T > 100 K. The possible origins of this phenomenon were discussed in detail. The occurrence of the AFM to SG-like magnetic transition is associated with the combination of chemical disorder due to a randomized substitution of Cd with Mg and the orientational disorder of the Cd4 tetrahedra.