  A search is conducted for new resonances decaying into a $W$ or $Z$ boson and
a 125 GeV Higgs boson in the $\nu\bar{\nu}b\bar{b}$, $\ell^{\pm}{\nu}b\bar{b}$,
and $\ell^+\ell^-b\bar{b}$ final states, where $\ell^{\pm}= e^{\pm}$ or
$\mu^{\pm}$, in $pp$ collisions at $\sqrt{s} = 13$ TeV. The data used
correspond to a total integrated luminosity of 36.1 fb$^{-1}$ collected with
the ATLAS detector at the Large Hadron Collider during the 2015 and 2016
data-taking periods. The search is conducted by examining the reconstructed
invariant or transverse mass distributions of $Wh$ and $Zh$ candidates for
evidence of a localised excess in the mass range of 220 GeV up to 5 TeV. No
significant excess is observed and the results are interpreted in terms of
constraints on the production cross-section times branching fraction of heavy
$W^\prime$ and $Z^\prime$ resonances in heavy-vector-triplet models and the
CP-odd scalar boson $A$ in two-Higgs-doublet models. Upper limits are placed at
the 95% confidence level and range between $9.0\times 10^{-4}$ pb and
$8.1\times 10^{-1}$ pb depending on the model and mass of the resonance.
