We explore the effect of the magnetic field when using realistic three-dimensional convection experiments to determine solar element abundances. By carrying out magnetoconvection simulations with a radiation-hydro code (the Copenhagen stagger code) and through a posteriori spectral synthesis of three Fe I lines, we obtain evidence that moderate amounts of mean magnetic flux cause a noticeable change in the derived equivalent widths compared with those for a non-magnetic case. The corresponding Fe abundance correction for a mean flux density of 200 G reaches up to ~0.1 dex in magnitude. These results are based on space- and time-averaged line profiles over a time span of 2.5 solar hours in the statistically stationary regime of the convection. The main factors causing the change in equivalent widths, namely the Zeeman broadening and the modification of the temperature stratification, act in different amounts and, for the iron lines considered here, in opposite directions; yet, the resulting |Δlog epsilonsun(Fe)| coincides within a factor of 2 in all of them, even though the sign of the total abundance correction is different for the visible and infrared lines. We conclude that magnetic effects should be taken into account when discussing precise values of the solar and stellar abundances and that an extended study is warranted.