  The dark matter relic density may be governed by the presence of new
mediators that connect the dark matter field with the Standard Model particles.
When the dark matter particle mass is larger than the mediator's, the pair
production of mediators is kinematically open. This setup is known in the
literature as secluded dark matter. Motivated by the appearance of secluded
dark matter in several model building endeavours, we investigate the
sensitivity of TeV gamma-ray instruments in the Southern Hemisphere namely,
H.E.S.S., CTA, and SWGO to secluded dark matter annihilating in the Galactic
Halo. We exploit the complementarity aspects of these detectors to find
restrictive bounds on the annihilation cross-section for different annihilation
channels. In particular, for a dark matter particle mass of $2$~TeV, H.E.S.S.
is able to constraint $\langle \sigma v \rangle \geq 4 \times 10^{-26}\,\, {\rm
cm}^3\, {\rm s}^{-1}$ at 95\% confidence level for the $4q$ and $4\tau$
channel, while CTA will be sensitive to $\langle \sigma v \rangle \geq 7 \times
10^{-27}\,\, {\rm cm}^3\, {\rm s}^{-1}$ and SWGO $\langle \sigma v \rangle \geq
6 \times 10^{-27}\,\, {\rm cm}^3\, {\rm s}^{-1}$ for the $4\tau$ channel, both
well below the thermal relic cross-section. In fact, the combination of CTA and
SWGO will be able to probe cross-sections below the thermal relic value for
dark matter particles in the whole mass range between 100 GeV and 100 TeV in
the $4q$ and $4\tau$ channels, and between 100 GeV and $\sim$40 TeV in the $4b$
channel.
