Optical communication wavelength is being extended from the near-infrared band of 1.31/1.55 µm to the mid-infrared band of 2 µm or beyond for satisfying the increasing demands for high-capacity long-distance data transmissions. An efficient electro-optic (EO) modulator working at 2 µm is highly desired as one of the indispensable elements for optical systems. Lithium niobate (LiNbO3) with a large second-order nonlinear coefficient is widely used in various EO modulators. Here, we experimentally demonstrate the first Mach-Zehnder EO modulator working at 2 µm based on the emerging thin-film LiNbO3 platform. The demonstrated device exhibits a voltage-length product of 3.67 V·cm and a 3-dB-bandwidth of >22 GHz which is limited by the 18 GHz response bandwidth of the photodetector available in the lab. Open eye-diagrams of the 25 Gb/s on-off keying (OOK) signals modulated by the fabricated Mach-Zehnder EO modulator is also measured experimentally with a SNR of about 14 dB.