In this work, we focus on the study of the structural and elastic properties of mercury digallium sulfide (HgGa2S4) at high pressures. This compound belongs to the family of AB(2)X(4) ordered-vacancy compounds and exhibits a tetragonal defect chalcopyrite structure. X-ray diffraction measurements at room temperature have been performed under compression up to 15.1 GPa in a diamond anvil cell. Our measurements have been complemented and compared with ab initio total energy calculations. The axial compressibility and the equation of state of the low-pressure phase of HgGa2S4 have been experimentally and theoretically determined and compared to other related ordered-vacancy compounds. The pressure dependence of the theoretical cation-anion and vacancy-anion distances and compressibilities in HgGa2S4 are reported and discussed in comparison to other related ordered-vacancy compounds. Finally, the pressure dependence of the theoretical elastic constants and elastic moduli of HgGa2S4 has been studied. Our calculations indicate that the low-pressure phase of HgGa2S4 becomes mechanically unstable above 13.8 GPa.