The low-temperature magnetic properties of the Ce atoms in the intermetallic compounds CeMn₂Ge₂ and CeMn₂Si₂ were studied. Previous neutron scattering measurements did not detect an ordered moment at Ce atoms in either compound despite the fact that they are surrounded by the Mn moments ordered ferromagnetically in the CeMn₂Ge₂ and antiferromagnetically in the CeMn₂Si₂. Contrasting with this result, a recent measurement performed with the time differential perturbed angular correlation (TDPAC) technique showed the presence of a pronounced magnetic hyperfine field (MHF) at Ce sites in the CeMn₂Ge₂ compound and no MHF in CeMn₂Si₂. The absence of the Ce magnetic moment and MHF in the silicide can be understood in terms of too weak a Ce–Ce magnetic interaction while in the germanide the TDPAC result suggests that some magnetic ordering of Ce atoms may occur. Aiming to understand the effects which result in the quenching of the Ce 4f moment in both cases, we performed first-principles band-structure calculations for both systems, using the full potential linear augmented plane wave method. It is shown that the magnetism of the Ce sublattice has fundamentally different nature in CeMn₂Si₂ and CeMn₂Ge₂. While the Ce atoms are intrinsically non-magnetic in the silicide, having a zero magnetic moment with both spin and orbital contributions identically zero, they display magnetic properties in the CeMn₂Ge₂ since their very small total moment is composed of finite spin and orbital components which almost cancel each other accidentally.