Most chemical abundance determinations ignore that the solar photosphere is significantly magnetized by the ubiquitous presence of a small-scale magnetic field. A recent investigation has suggested that there should be a significant impact on the derived iron abundance, owing to the magnetically induced changes on the photospheric temperature and density structure (indirect effect). The three-dimensional (3D) photospheric models used in that investigation have non-zero net magnetic flux values and stem from magneto-convection simulations without small-scale dynamo action. Here we address the same problem by instead using 3D models of the quiet solar photosphere that result from a state-of-the-art magneto-convection simulation with small-scale dynamo action, where the net magnetic flux is zero. One of these 3D models has negligible magnetization, while the other is characterized by a mean field strength of 160 Gauss in the low photosphere. With such 3D models we carried out spectral synthesis for a large set of Fe i lines to derive abundance corrections, taking the above-mentioned indirect effect and the Zeeman broadening of the intensity profiles (direct effect) into account. We conclude that if the magnetism of the quiet solar photosphere is mainly produced by a small-scale dynamo, then its impact on the determination of the solar iron abundance is negligible. Table 1 is available in electronic form at http://www.aanda.org