Mid-infrared photonics in silicon needs low-loss integrated waveguides. While monocrystalline germanium waveguides on silicon have been proposed, experimental realization has not been reported. Here we demonstrate a germanium strip waveguide on a silicon substrate. It is designed for single mode transmission of light in transverse magnetic (TM) polarization generated from quantum cascade lasers at a wavelength of 5.8 μm. The propagation losses were measured with the Fabry–Perot resonance method. The lowest achieved propagation loss is 2.5 dB=cm, while the bending loss is measured to be 0.12 dB for a 90° bend with a radius of 115 μm.