The orbital-free frozen-density embedding scheme within density-functional theory [ T. A. Wesolowski and A. Warshel, J. Phys. Chem. 97, 8050 (1993) ] is applied to the calculation of induced dipole moments of the van der Waals complexes CO₂⋯X (X = He, Ne, Ar, Kr, Xe, Hg). The accuracy of the embedding scheme is investigated by comparing to the results of supermolecule Kohn-Sham density-functional theory calculations. The influence of the basis set and the consequences of using orbital-dependent approximations to the exchange-correlation potential in embedding calculations are examined. It is found that in supermolecular Kohn-Sham density-functional calculations, different common approximations to the exchange-correlation potential are not able to describe the induced dipole moments correctly and the reasons for this failure are analyzed. It is shown that the orbital-free embedding scheme is a useful tool for applying different approximations to the exchange-correlation potential in different subsystems and that a physically guided choice of approximations for the different subsystems improves the calculated dipole moments significantly.