  We show that the magnetic analogue of the R\"{a}dler effect of mean-field
dynamo theory leads to a non-linear backreaction that quenches a large-scale
galactic dynamo, and can result in saturation of the large-scale magnetic field
at near-equipartition with turbulent kinetic energy density. In a rotating
fluid containing small-scale magnetic fluctuations, anisotropic terms in the
mean electromotive force are induced via the Coriolis effect and these terms
lead to a reduction of the growth rate in a predominantly $\alpha\Omega$-type
galactic dynamo (Chamandy & Singh 2017). By including the generation of
small-scale magnetic fluctuations by turbulent tangling of the large-scale
magnetic field, one obtains a negative feedback effect that quenches the dynamo
and leads to the saturation of the large-scale field. This saturation mechanism
is found to be competitive with the dynamical $\alpha$-quenching mechanism for
realistic galactic parameter values. Furthermore, in the context of the
dynamical $\alpha$-quenching model, a separate non-linear term is obtained
which has the same form as the helicity flux term of Vishniac & Cho (2001), but
which depends on the strength of small-scale magnetic fluctuations. We briefly
discuss the observational implications of the magnetic R\"{a}dler effect for
galaxies.
