The relativistic effect on interaction-induced dipole moment and polarizability in the HF...AuH dimer is studied in the framework of the long-range perturbation theory model and by using the supermolecular approach. The perturbation treatment is limited to the lowest multipole-expanded form known as the dipole-induced-dipole (DID) approximation. Although the long-range DID model may be useful in elucidating the origin of the relativistic effect on interaction-induced electric properties, it fails to predict the correct magnitude of this effect for all but very large separations between the two subsystems. At intermediate monomer separations the supermolecular model predicts a substantial relativistic contribution to interaction-induced dipole moments and a rather moderate relativistic effect on induced polarizabilities. It has also been found that the vibrational contribution to the interaction-induced polarizability estimated in the double harmonic approximation may dominate over the changes in the pure electronic term. However, sufficiently accurate calculations of the vibrational contribution to electric properties of a weakly bound dimer, which would confirm this finding, appear to be unlikely at present.