We demonstrate third harmonic generation in plasmonic antennas consisting of highly doped germanium grown on silicon substrates and designed to be resonant in the mid-infrared frequency range that is inaccessible with conventional nonlinear plasmonic materials. Owing to the near-field enhancement, the result is an ultrafast, subdiffraction, coherent light source with a wavelength tunable between 3 and 5 µm, and ideally overlapping with the fingerprint region of molecular vibrations. To observe the nonlinearity in this challenging spectral window, a high-power femtosecond laser system equipped with parametric frequency conversion in combination with an all-reflective confocal microscope setup is employed. We demonstrate spatially resolved maps of the linear scattering cross section and the nonlinear emission of single isolated antenna structures. A clear third-order power dependence as well as mid-infrared emission spectra prove the nonlinear nature of the light emission. Simulations support the observed resonance length of the double-rod antenna and demonstrate that the field enhancement inside the antenna material is responsible for the nonlinear frequency mixing.