Characterising quantum states of light in the 2 µm band requires high-performance shot-noise limited detectors. Here, we present the characterisation of a homodyne detector that we use to observe vacuum shot-noise via homodyne measurement with a 2.07 µm pulsed mode-locked laser. The device is designed primarily for pulsed illumination. It has a 3-dB bandwidth of 13.2 MHz, total conversion efficiency of 57% at 2.07 µm, and a common-mode rejection ratio of 48 dB at 39.5 MHz. The detector begins to saturate at 1.8 mW with 9 dB of shot-noise clearance at 5 MHz. This demonstration enables the characterisation of megahertz-quantum optical behaviour in the 2 µm band and provides a guide of how to design a 2 µm homodyne detector for quantum applications.