We present results of a deep mid-infrared survey in the SSA13 field with the Infrared Space Observatory (ISO). In order to probe the near-infrared light at high redshifts, we surveyed the field with the broad band LW2 (5-8.5um) filter of the mid-infrared camera ISOCAM. Adopting a highly redundant imaging strategy for the 23 hour observation and carefully treating gradual changes in the detector responsivity caused by a very high rate of cosmic ray impacts, we succeeded in reaching an 80% completeness limit of 16uJy in the central 7 arcmin2 region. Utilizing the signal-to-noise ratio map, we detected 65 sources down to 6uJy in the 16 arcmin2 field. Integral galaxy number counts at 6.7um are then derived, reaching 1.3e4/deg2 at the faint limit with a slope of -1.6 between 13uJy and 130uJy. Integrating individual sources in this flux range, the resolved fraction of the extragalactic background light at 6.7um is estimated to be 0.56nW/m2/sr. These results, which reach a flux limit three times fainter than those in the Hubble Deep Fields, are in fairly good agreement with a model prediction by Franceschini et al. (1997). Finally, we discuss the relation of distant massive E/S0 galaxies to the faint 6.7um galaxy population.