In this paper, we present a thorough investigation of vibrational, structural, and electronic properties of perovskite-type rhombohedral ${\mathrm{Ba}}_{2}{\mathrm{ZnTeO}}_{6}$ (BZTO) under systematic application of pressure. To carry out the analysis, we have performed pressure-dependent Raman spectroscopic measurements, synchrotron x-ray diffraction, and density functional theory (DFT)-based calculations. At ambient conditions, BZTO stabilizes in $R\overline{3}m$ space group, which under pressure undergoes a structural transition to a monoclinic phase with space group $C2/m$ at around 18 GPa. In-depth Raman analysis reveals softening of a phonon mode ${\mathrm{E}}_{g}$ ($\ensuremath{\sim}28\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$) leads to the structural phase transition. First-principles DFT calculations also indicate that the doubly degenerate soft mode associated with the in-phase ${\mathrm{TeO}}_{6}$ octahedral rotation drives the structure to a lower symmetry phase $C2/m$.