Nonlinear photonic devices are critical for many integrated infrared platform applications such as supercontinuum generation and frequency combs. It also holds the promise of all-optical modulators that will surpass by orders of magnitude the current devices. Typically, these devices rely on Si material platforms that suffer from high nonlinear losses due to two-photon absorption (TPA). A novel, hybrid ZnTe-on-Si waveguide system is demonstrated and fully characterized via ellipsometry and a combination of a bidirectional top-hat spectral broadening measurement and a dispersive scan (D-Scan) experiment to extract the effective TPA coefficient ($\beta_{TPA}$) and optical Kerr coefficient (n 2 ) of the hybrid waveguide system. The experimentally characterized $\beta_{TPA}$=S.76x1$0^{-13}$m/W of this ZnTe-on-Si system is an order of magnitude lower than pure Si waveguides with a comparable nonlinear Kerr coefficient, providing a promising material platform for future high-performance, low-loss, compact, integrated nonlinear infrared devices.