  We analytically model the non-linear effects induced by massive neutrinos on
the total matter power spectrum using the halo model reaction framework of
Cataneo et al. 2019. In this approach the halo model is used to determine the
relative change to the matter power spectrum caused by new physics beyond the
concordance cosmology. Using standard fitting functions for the halo abundance
and the halo mass-concentration relation, the total matter power spectrum in
the presence of massive neutrinos is predicted to percent-level accuracy, out
to $k=10 \, h \, {\rm Mpc}^{-1}$. We find that refining the prescriptions for
the halo properties using $N$-body simulations improves the recovered accuracy
to better than 1%. This paper serves as another demonstration for how the halo
model reaction framework, in combination with a single suite of standard
$\Lambda$CDM simulations, can recover percent-level accurate predictions for
beyond-$\Lambda$CDM matter power spectra, well into the non-linear regime.
