The structure and stretching frequency of the CO molecule physisorbed on the MgO(100) surface were investigated using the recently developed formalism of Kohn-Sham equations with constrained electron density (KSCED). The KSCED method makes it possible to divide a large system into two subsystems and to study one of them using Kohn-Sham-like equations in which the effective potential takes into account the interactions between subsystems. Compared to the standard Kohn-Sham formalism, the KSCED method involves an additional functional due to the non-additivity of the kinetic energy. The surface was represented using a cluster ((MgO5)8− or Mg9O9) embedded in an array of electric point-charges. The KSCED calculations led to a blue-shift of the stretching frequency of the C-down adsorbed CO molecule amounting to 47–21 cm−1 depending on the distance from the surface. At the C–Mg distance of 2.42 Å, which corresponds to a typical minimum of the potential energy curve derived from supermolecule Kohn-Sham calculations applying gradient-corrected functionals, the KSCED frequency shift amounts to 35 cm−1 in excellent agreement with the most recent experiments. The CO stretching frequency of the O-down adsorbed CO molecule is red-shifted. The effects of cluster size and choice of the functionals on the KSCED frequencies, geometries and energies were analyzed. For C–Mg distances varying between 2.3 and 3.0 Å, changing the cluster size affects the frequencies by less than 4 cm−1 and the CO bond length by less than 0.0003 Å. At C–Mg distances larger than 2.4 Å, the change of the cluster size negligibly affects the KSCED interaction energies. The KSCED formalism makes it possible to study directly the effects associated with relaxation of the surface's electron density upon adsorbing CO. It is shown that these effects might contribute up to 30% of the KSCED interaction energy, but that they do not result in significant changes of either the geometries or frequencies.