Gamma-ray line signatures can be expected in the very-high-energy (${E}_{\ensuremath{\gamma}}>100\text{ }\text{ }\mathrm{GeV}$) domain due to self-annihilation or decay of dark matter (DM) particles in space. Such a signal would be readily distinguishable from astrophysical $\ensuremath{\gamma}$-ray sources that in most cases produce continuous spectra that span over several orders of magnitude in energy. Using data collected with the H.E.S.S. $\ensuremath{\gamma}$-ray instrument, upper limits on linelike emission are obtained in the energy range between $\ensuremath{\sim}500\text{ }\text{ }\mathrm{GeV}$ and $\ensuremath{\sim}25\text{ }\text{ }\mathrm{TeV}$ for the central part of the Milky Way halo and for extragalactic observations, complementing recent limits obtained with the Fermi-LAT instrument at lower energies. No statistically significant signal could be found. For monochromatic $\ensuremath{\gamma}$-ray line emission, flux limits of $(2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}--2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5})\text{ }\text{ }{\mathrm{m}}^{\ensuremath{-}2}\text{ }{\mathrm{s}}^{\ensuremath{-}1}\text{ }{\mathrm{sr}}^{\ensuremath{-}1}$ and $(1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}--2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6})\text{ }\text{ }{\mathrm{m}}^{\ensuremath{-}2}\text{ }{\mathrm{s}}^{\ensuremath{-}1}\text{ }{\mathrm{sr}}^{\ensuremath{-}1}$ are obtained for the central part of the Milky Way halo and extragalactic observations, respectively. For a DM particle mass of 1 TeV, limits on the velocity-averaged DM annihilation cross section $⟨\ensuremath{\sigma}v{⟩}_{\ensuremath{\chi}\ensuremath{\chi}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}}$ reach $\ensuremath{\sim}{10}^{\ensuremath{-}27}\text{ }\text{ }{\mathrm{cm}}^{3}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$, based on the Einasto parametrization of the Galactic DM halo density profile.