Dwarf galaxies are widely believed to be among the best targets for indirect dark matter searches using high-energy gamma rays; and indeed gamma-ray emission from these objects has long been a subject of detailed study for ground-based atmospheric Cherenkov telescopes. Here, we update current exclusion limits obtained on the closest dwarf, the Sagittarius dwarf galaxy, in light of recent realistic dark matter halo models. The constraints on the velocity-weighted annihilation cross section of the dark matter particle are of a few 10$^{-23}$ cm$^{3}$s$^{-1}$ in the TeV energy range for a 50 h exposure. The limits are extrapolated to the sensitivities of future Cherenkov Telescope Arrays. For 200 h of observation time, the sensitivity at 95% C.L. reaches 10$^{-25}$ cm$^{3}$s$^{-1}$. Possible astrophysical backgrounds from gamma-ray sources dissembled in Sagittarius dwarf are studied. It is shown that with long-enough observation times, gamma-ray background from millisecond pulsars in a globular cluster contained within Sagittarius dwarf may limit the sensitivity to dark matter annihilations.
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