Metamaterial perfect absorbers (MPAs) are artificial materials composed of an array of subwavelength structures that manipulate electromagnetic waves to achieve extraordinary light absorption properties. Driven by the advent of the Internet of Things, MPAs are employed in microelectromechanical systems for the development of efficient and miniaturized IR detectors, imagers, and spectrometers, thanks to their lithographically tunable peak absorption, spectral selectivity, and ultrathin thickness. MPAs characterized by high absorptance in narrow spectral bands are particularly desirable for the implementation of high‐resolution IR spectroscopic sensors. Yet, no accurate analytical model is currently available to guide the design of an MPA with ultra‐narrow absorption bandwidth, while meeting all the stringent requirements for spectroscopic sensors. Here, a circuit model capable of accurately predicting spectral responses of metal–insulator–metal (MIM) IR absorbers is reported. The model is experimentally validated in the mid‐wavelength IR spectral range and exploited for the first demonstration of an MIM IR absorber that exhibits performance approaching the predicted physical limits: full‐width at half‐maximum ≈3% and near‐unity absorption (η > 99.7%) at 5.83 µm wavelength, while independent of incident angle and polarization of the impinging IR radiation. These unprecedented absorption properties are key enablers for the development of miniaturized, low‐cost, and high‐resolution spectrometers.