We use the unprecedented resolution and depth of the JWST NIRCam Early Release Observations at 1-5 mu m to study the stellar mass, age, and metallicity of compact star clusters in the neighborhood of the host galaxies in the SMACS J0723.3-7327 galaxy cluster field at z = 0.39. The measured colors of these star clusters show a similar distribution as quiescent galaxies at the same redshift, but are > 3 mag fainter than the current depths of wide-field galaxy survey. The star clusters are unresolved in the NIRCam/F150W data suggesting sizes smaller than 50 pc. This is significantly smaller than star-forming clumps or dwarf galaxies in local galaxies. From fitting their photometry with simple stellar population (SSP) models, we find stellar metallicities consistent with 0.2-0.3 Z(? )and ages of 1.5(-0.5)(+0.5)Gyr Z(?) and solar/supersolar at 4 sigma significance. Assuming mass-to-light ratios obtained from the best-fit SSP, we estimate stellar masses of 2.4(-1.5)(+3.0)x10(6)M(? )z = 0.5-0.7, which could have been subsequently stripped away from their host galaxies due to interactions in the cluster environment or formed in cold flows onto the cluster core. However, we cannot rule out these objects being compact cores of stripped dwarf galaxies.