The MeerKAT Absorption Line Survey (MALS) has observed 391 telescope pointings at the L band (900-1670MHz) at {delta}<~+20{deg}. We present radio continuum images and a catalog of 495325 (240321) radio sources detected at a signal-to-noise ratio (S/N)>5 over an area of 2289deg^2^ (1132deg^2^) at 1006MHz (1381MHz). Every MALS pointing contains a central bright radio source (S_1GHz_>~0.2Jy). The median spatial resolution is 12" (8"). The median rms noise away from the pointing center is 25{mu}Jy/beam (22{mu}Jy/beam) and is within ~15% of the achievable theoretical sensitivity. The flux density scale ratio and astrometric accuracy deduced from multiply observed sources in MALS are <1% (8% scatter) and 1", respectively. Through comparisons with NVSS and FIRST at 1.4GHz, we establish the catalog's accuracy in the flux density scale and astrometry to be better than 6% (15% scatter) and 0.8", respectively. The median flux density offset is higher (9%) for an alternate beam model based on holographic measurements. The MALS radio source counts at 1.4GHz are in agreement with literature. We estimate spectral indices ({alpha}) of a subset of 125621 sources (S/N>8), confirm the flattening of spectral indices with decreasing flux density, and identify 140 ultra-steep-spectrum ({alpha}{<}-1.3) sources as prospective high-z radio galaxies (z>2). We have identified 1308 variable and 122 transient radio sources comprising primarily active galactic nuclei that demonstrate long-term (26yr) variability in their observed flux densities.