We have theoretically demonstrated that hybridization of phonon modes in Si/Ge core/shell nanowires and corresponding decrease of average phonon group velocity lead to the suppression of phonon thermal conductivity in Si/Ge core/shell nanowires in comparison with generic homogeneous silicon nanowires. The phonon energy spectra were calculated using the Valence Force Field model of lattice vibrations, while thermal conductivities were obtained from the Boltzmann transport equation within the relaxation time approximation. Our results indicate that core/shell nanowires are good candidates for the efficient phonon engineering of their phonon and thermal properties.