The CM Draconis system comprises two eclipsing mid-M dwarfs of nearly equal mass in a 1.27-day orbit. This well-studied eclipsing binary has often been used for benchmark tests of stellar models, since its components are amongst the lowest mass stars with well-measured masses and radii (~ 1% relative precision). However, as with many other low-mass stars, non-magnetic models have been unable to match the observed radii and effective temperatures for CM Dra at the 5-10% level. To date, the uncertain metallicity of the system has complicated comparison of theoretical isochrones with observations. In this Letter, we use data from the SpeX instrument on the NASA Infrared Telescope Facility (IRTF) to measure the metallicity of the system during primary and secondary eclipses, as well as out of eclipse, based on an empirical metallicity calibration in the H and K near-infrared (NIR) bands. We derive a [Fe/H] = -0.30 +- 0.12 that is consistent across all orbital phases. The determination of [Fe/H] for this system constrains a key dimension of parameter space when attempting to reconcile model isochrone predictions and observations