In this paper, a carrier-injection electro-absorption modulator (EAM) at 2 µm is demonstrated on Ge-on-Si platform. The EAM shows a compact size and high modulation efficiency due to the strong free-carrier electroabsorption (FCEA) effect in Ge. A modulation depth of 40 dB can be obtained under the injection current of only 420 mA. Small-signal frequency response measurement is performed and a small-signal equivalent circuit model is proposed. Based on reflection coefficients and equivalent circuit, the frequency response of carrier-injection EAM is discussed in detail. The 500 Mbps open eye diagram verifies the data-processing capacity of our EAM at 2 µm wavelength for its application in biological, chemical molecular detection, and infrared imaging systems.