The MACE (Major Atmospheric Cherenkov Experiment) telescope has started its regular gamma-ray observations at Hanle in India. Located at an altitude of ∼ 4.3 km above sea level and equipped with a 21 m diameter large quasi-parabolic reflector, it has the capability to explore the gamma-ray sky in the energy range above 20 GeV with very high sensitivity. In this work, we present the results from the feasibility studies for searching high-energy gamma-ray signals from dark matter interaction in potential astrophysical environments. We study the impact of MACE response function and other instrumental characteristics to probe the velocity average interaction cross-section (< σv >) of the weakly interacting massive particles (WIMPs), expected from the thermal dark matter freeze-out during the decoupling era. We consider the presence of dark matter in the form of pure WIMPs in the mass range 200 GeV - 10 TeV to produce distinctive gamma-ray spectra through its self-annihilation into standard model particles using the Pythia simulation package. The convolution of gamma-ray spectra corresponding to different standard model channels with the MACE response function is used to estimate the upper limit on < σv > for 100 hours of expected MACE observation of Segue1 (a dwarf spheroidal galaxy) which is a potential site of dark matter.