  We present the first scaling relation between weak-lensing galaxy cluster
mass, $M_{WL}$, and near-infrared luminosity, $L_K$. Our results are based on
17 clusters observed with wide-field instruments on Subaru, the United Kingdom
Infrared Telescope, the Mayall Telescope, and the MMT. We concentrate on the
relation between projected 2D weak-lensing mass and spectroscopically confirmed
luminosity within 1Mpc, modelled as $M_{WL} \propto L_{K}^b$, obtaining a power
law slope of $b=0.83^{+0.27}_{-0.24}$ and an intrinsic scatter of
$\sigma_{lnM_{WL}|L_{K}}=10^{+8}_{-5}\%$. Intrinsic scatter of ~10% is a
consistent feature of our results regardless of how we modify our approach to
measuring the relationship between mass and light. For example, deprojecting
the mass and measuring both quantities within $r_{500}$, that is itself
obtained from the lensing analysis, yields
$\sigma_{lnM_{WL}|L_{K}}=10^{+7}_{-5}\%$ and $b=0.97^{+0.17}_{-0.17}$. We also
find that selecting members based on their (J-K) colours instead of
spectroscopic redshifts neither increases the scatter nor modifies the slope.
Overall our results indicate that near-infrared luminosity measured on scales
comparable with $r_{500}$ (typically 1Mpc for our sample) is a low scatter and
relatively inexpensive proxy for weak-lensing mass. Near-infrared luminosity
may therefore be a useful mass proxy for cluster cosmology experiments.
