Most studies of the solar metallicity, based on abundance determinations of the CNO elements, ignore the fact that the quiet solar photosphere is significantly magnetized by a small-scale magnetic field with a mean field strength of ~100 G. Here we quantify how this significant magnetization affects determinations of the abundances of these chemical elements. To this end, we used two three-dimensional models of the solar photosphere taken from a magneto-convection simulation with small-scale dynamo action, one virtually unmagnetized, and the other characterized by a mean field strength of 160 G in the low photosphere. We performed local thermodynamic equilibrium spectral synthesis for a large set of C i, N i, and O i lines to derive abundance corrections. We included the magnetic broadening of the lines (direct effect) and the magnetically induced changes of the photospheric temperature stratification (indirect effect). We find that these small-scale dynamo magnetic fields only negligibly affect the determination of the solar abundances of carbon, nitrogen, and oxygen.