  We study the constraints that electroweak precision data can impose, after
the discovery of the Higgs boson by the LHC, on neutrinophilic
two-Higgs-doublet models which comprise one extra $SU(2)\times U(1)$ doublet
and a new symmetry, namely a spontaneously broken $\mathbb{Z}_2$ or a softly
broken global $U(1)$. In these models the extra Higgs doublet, via its very
small vacuum expectation value, is the sole responsible for neutrino masses. We
find that the model with a $\mathbb{Z}_2$ symmetry is basically ruled out by
electroweak precision data, even if the model is slightly extended to include
extra right-handed neutrinos, due to the presence of a very light scalar. While
the other model is still perfectly viable, the parameter space is considerably
constrained by current data, specially by the $T$ parameter. In particular, the
new charged and neutral scalars must have very similar masses.
