  The correction to the area law for the bipartite min-entanglement entropy of
weakly and locally interacting fermions is calculated based on a perturbative
extension of the flow equation holography method. Explicit calculations for the
one- and two-dimensional case (and similarly for higher dimensions) show that
the leading correction to the entanglement entropy of non-interacting fermions
up to $U^2$ in the interaction strength does not change the scaling, but only
affects the pre-factor of the leading logarithmic term multiplying it by the
quasiparticle residue. A term sub-leading to the area law is also present. It
is proportional to $U^2$ in the interaction strength and scales linearly with
the system size.
