In this paper, we have done a comparative theoretical study of electronic and magnetic properties of iron phthalocyanine (FePc) and cobalt phthalocyanine (CoPc) molecules physisorbed on a monolayer of MoS2 and graphene by density functional theory. Various types of physisorption sites have been considered for both surfaces. The lowest energy structure for both metal phthalocyanine (MPc) molecules physisorbed on MoS2 is a sulfur-top position, i.e., when the metal center of the molecule is on top of a sulfur atom. However, on graphene, the lowest energy structure for the FePc molecule is when a metal atom is on top of a bridge position. In contrast to this, the CoPc molecule prefers a carbon-top position. The adsorption of MPc molecules is stronger on the MoS2 surface than on graphene (∼2.5 eV higher physisorption energy). In these systems, spin dipole moments of the metal centers are antiparallel to the spin moments and hence a huge reduction of effective spin moment can be seen. The calculations of magnetic anisotropy energies using both variational and second-order perturbation approaches indicate no significant changes after physisorption. In case of the FePc and CoPc physisorption, respectively, an out-of-plane and an in-plane easy axis of magnetization can be observed. Our calculations indicate a reduction of MoS2 work function ∼1 eV due to physisorption of MPc molecules while it does not change significantly in the case of graphene.