We provide an upper bound on the ℓ2-torsion of a free-by-cyclic group, −ρ(2)(𝔽⋊Φℤ), in terms of a relative train-track representative for Φ∈Aut(𝔽). Our result shares features with a theorem of L\"uck-Schick computing the ℓ2-torsion of the fundamental group of a 3-manifold that fibers over the circle in that it shows that the ℓ2-torsion is determined by the exponential dynamics of the monodromy. In light of the result of L\"uck-Schick, a special case of our bound is analogous to the bound on the volume of a 3-manifold that fibers over the circle with pseudo-Anosov monodromy by the normalized entropy recently demonstrated by Kojima-McShane.