Despite the ubiquity of M dwarfs and their growing importance to studies of exoplanets, Galactic evolution, and stellar structure, methods for precisely measuring their fundamental stellar properties remain elusive. Existing techniques for measuring M dwarf luminosity, mass, radius, or composition are calibrated over a limited range of stellar parameters or require expensive observations. We find a strong correlation between the K_S_-band luminosity (M_K_), the observed strength of the I-band sodium doublet absorption feature, and [Fe/H] in M dwarfs without strong H{alpha} emission. We show that the strength of this feature, coupled with [Fe/H] and spectral type, can be used to derive M dwarf M_K_ and radius without requiring parallax. Additionally, we find promising evidence that the strengths of the I-band sodium doublet and the nearby I-band calcium triplet may jointly indicate {alpha}-element enrichment. The use of these I-band features requires only moderate-resolution near-infrared spectroscopy to provide valuable information about the potential habitability of exoplanets around M dwarfs, and surface gravity and distance for M dwarfs throughout the Galaxy. This technique has immediate applicability for both target selection and candidate planet-host system characterization for exoplanet missions such as TESS and K2.