We report here the first demonstration of a cryogenic mid-wave infrared (MWIR) hyperspectral fixed-cavity Fabry-Perot filter based on a suspended tensile-strained single-layer 2-D subwavelength grating (SWG) mirror. Optical design optimization of the 2-D SWG mirror and parameter tolerance study are performed. For the first time, process control of grating air-hole sidewall angle and the grating air-hole fill-factor fabrication error caused by e-beam lithography electron-scattering effect is reported. At 80 K, namely the operating temperature of MWIR photodetectors, the as-fabricated suspended 2-D SWG mirror has achieved excellent surface flatness with a slight center-to-edge bowing of 15 nm over a 1-mm2 large mirror area and a high average reflectivity of 0.97 across a wavelength range of 3.72-5 µm, which represents an unprecedentedly wide fractional bandwidth Δλ/λc of 30%. The cryogenically cooled Fabry-Perot filter exhibits an unrivaled high spectral resolution of 10 nm that far exceeds the optical requirement for MWIR hyperspectral imaging applications.