Monochromatic gamma-ray signals constitute a potential smoking gun signature for
annihilating or decaying dark matter particles that could relatively easily be distinguished from
astrophysical or instrumental backgrounds. We provide an updated assessment of the sensitivity of
the Cherenkov Telescope Array (CTA) to such signals, based on observations of the Galactic centre
region as well as of selected dwarf spheroidal galaxies. We find that current limits and
detection prospects for dark matter masses above 300 GeV will be significantly improved, by up to
an order of magnitude in the multi-TeV range. This demonstrates that CTA will set a new standard
for gamma-ray astronomy also in this respect, as the world's largest and most sensitive
high-energy gamma-ray observatory, in particular due to its exquisite energy resolution at TeV
energies and the adopted observational strategy focussing on regions with large dark matter
densities. Throughout our analysis, we use up-to-date instrument response functions, and we
thoroughly model the effect of instrumental systematic uncertainties in our statistical
treatment. We further present results for other potential signatures with sharp spectral features,
e.g. box-shaped spectra, that would likewise very clearly point to a particle dark matter origin.