We present a high-resolution (0.6″) 2.2 μm (K-band) image of the central (∼750 pc) circumnuclear region of the starburst galaxy NGC 1808. Contrary to previous lower resolution observations our image reveals detailed structure in the distribution of near-infrared light that is produced within the circumnuclear region. Our data reveal the presence of many distinct and compact (≲0.7″) near-infrared continuum sources spread throughout the circumnuclear region. These sources are likely individual clusters containing a few to several hundred massive (∼25-30 M⊙) red supergiants. The inferred cluster masses range from 105 to 106 M⊙. Together with previous 2.17 μm Brγ line observations we conclude that the circumnuclear clusters are young and that their rates of star-formation are decaying rapidly. The cluster ages are close to the "critical" age of 10 Myr at which clusters reach their maximum luminosities in the near-infrared. The individual stellar systems we have detected are probably gravitationally bound. They appear to be the first unambiguous detections of the IR counterparts of young clusters (possibly globular clusters) which have recently been identified in high-resolution optical and ultraviolet (HST) imaging of several types of starburst galaxies. A 500 pc long infrared bar, and evidence of inner spiral or ring-like structures are present in our image. The infrared bar is well aligned with a more extended (∼6 kpc) bar-structure visible in wide-field Ha and 21 cm emission line maps. A prominent, and just resolved, 2.2 μm continuum source is present at the galaxy nucleus. Most of the near-infrared light in the nuclear source is likely produced by massive red giants and supergiant stars. Both decaying and continuous modes of star formation are consistent with the observations. For the decaying mode the inferred age is 8 Myr with a burst mass of ∼5 × 106 M⊙ within the central 50 pc. For continuous star formation the inferred age is ∼200 Myr with a total accumulated mass of 3.2 × 107 M⊙. Continuous star formation may be fueled by gas inflow along the bar at a rate of ∼ 0.16 M⊙ yr-1.