A weak-lensing analysis of a wide-field V-band image centered on the cluster Abell 1942 (z=0.223) has uncovered the presence of a mass concentration projected ~ 7 arcminutes South of the cluster center. From an additional wide-field image, taken with a different camera in the I-band, the presence of this mass concentration is confirmed. A statistical analysis, using the aperture mass technique, shows that the probability of finding such a mass concentration at the observed position from a random alignment of background galaxies is 10^-6 and 4x 10^-4 for the V- and I-band image, respectively. No obvious strong concentration of bright galaxies is seen at the position of the mass concentration, but a slight galaxy number overdensity is present about 1' away from its center. Archival ROSAT-HRI data show the presence of a weak extended X-ray source near to the mass concentration, but also displaced by about 1' from its center, and very close to the center of the slight galaxy number concentration. From the spatial dependence of the tangential alignment around the center of the mass concentration, a rough mass estimate can be obtained which depends strongly on the assumed redshift of the lens and the redshift distribution of the galaxies which are used for measuring the lensing signal. A lower bound on the mass inside a sphere of radius 0.5 h^-1 Mpc is 1x 10¹⁴h^-1M_sun, considerably higher than crude mass estimates based on the X-ray data. Shifting the lens to higher redshift increases both the lensing and X-ray mass estimates, but does not resolve the mass discrepancy. Concerning the nature of the mass concentration, no firm conclusion can be drawn from the available data. If it were a high-redshift cluster, the weak X-ray flux would indicate that it had an untypically low X-ray luminosity for its mass; if the X-ray emission were physically unrelated to the mass concentration, e.g. coming from the relatively low-redshift group which shows up in the number density of galaxies, this conclusion would be even stronger. Since the search for massive halos by weak lensing enables us for the first time to select halos based on their mass properties only, it is possible that new types of objects can be detected, e.g. halos with very little X-ray and/or optical luminosity, should they exist. The mass concentration in the field of A1942 may be the first example of such a halo. Possibilities to establish the nature of this mass concentration with future observations are briefly discussed. based on observations with the Canada-France-Hawaii Telescope (CFHT) operated by the National Research Council of Canada (CNRC), the Institut des Sciences de l'Univers (INSU) of the Centre National de la Recherche Scientifique (CNRS) and the University of Hawaii (UH) and on data obtained through the NASA/GSFC HEASARC Online archive.