The recently proposed dynamical multiferroic effect describes the generation of magnetization from temporally varying electric polarization. Here, we show that the effect can lead to a magnetic field at moving ferroelectric domain walls, where the rearrangement of ions corresponds to a rotation of ferroelectric polarization in time. We develop an expression for the dynamical magnetic field, and calculate the relevant parameters for the example of 90$^circ$ and 180$^circ$ domain walls in BaTiO$_3$ using a combination of density functional theory and phenomenological modeling. We find that the magnetic field reaches the order of several $mu$T at the center of the wall, and we propose two experiments to measure the effect with nitrogen-vacancy center magnetometry.
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