  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 \textit{TESS} and
\textit{K2}.
