  We compute the tree-level bispectrum of dark matter in the presence of
massive neutrinos in the mildly non-linear regime in the context of the
effective field theory of large-scale structure (EFTofLSS). For neutrinos,
whose typical free streaming wavenumber ($k_{\rm fs}$) is longer than the
non-linear scale ($k_{\mathrm{NL}}$), we solve a Boltzmann equation coupled to
the effective fluid equation for dark matter. We solve perturbatively the
coupled system by expanding in powers of the neutrino density fraction
($f_{\nu}$) and the ratio of the wavenumber of interest over the non-linear
scale ($k/k_{\mathrm{NL}}$) and add suitable counterterms to remove the
dependence from short distance physics. For equilateral configurations, we find
that the total-matter tree-level bispectrum is approximately $16f_{\nu}$ times
the dark matter one on short scales ($k > k_{\rm fs}$). The largest
contribution stems from the back-reaction of massive neutrinos on the dark
matter growth factor. On large scales ($k < k_{\rm fs}$) the contribution of
neutrinos to the bispectrum is smaller by up to two orders of magnitude.
