  The current velocity of the Smith Cloud indicates that it has undergone at
least one passage of the Galactic disc. Using hydrodynamic simulations we
examine the present day structure of the Smith Cloud. We find that a dark
matter supported cloud is able to reproduce the observed present day neutral
hydrogen mass, column density distribution and morphology. In this case the
dark matter halo becomes elongated, owing to the tidal interaction with the
Galactic disc. Clouds in models neglecting dark matter confinement are
destroyed upon disc passage, unless the initial cloud mass is well in excess of
what is observed today. We then determine integrated flux upper limits to the
gamma-ray emission around such a hypothesised dark matter core in the Smith
Cloud. No statistically significant core or extended gamma-ray emission are
detected down to a 95% confidence level upper limit of $1.4\times10^{-10}$ ph
cm$^{-2}$ s$^{-1}$ in the 1-300 GeV energy range. For the derived distance of
12.4 kpc, the Fermi upper limits set the first tentative constraints on the
dark matter cross sections annihilating into $\tau^{+}{\tau}^{-}$ and
$b\bar{b}$ for a high-velocity cloud.
