The influence of three-photon absorption (3PA) on cross-phase modulation (XPM) effect in the mid-infrared (IR) region is theoretically investigated in silicon-on-sapphire (SOS) waveguides. It is found that the 3PA-induced nonlinear losses in the SOS waveguide will be considerable for the pulse propagation in the wavelength region of 2300 nm-3300 nm when the pump peak intensity is high enough. For the XPM process, the 3PA and 3PA-induced free-carrier effects can affect the spectrum and temporal profiles of the pump and signal pulses for sufficiently high pump peak intensities. Moreover, the XPM-induced frequency shift of signal spectrum is also discussed with different pump peak intensities, and the XPM-induced blue and red shifts are reduced due to 3PA.