Τhe magnetoelectric ZnCr2Se4 spinel, with space group Fd3m, undergoes a reversible first-order structural transition initiating at 17 GPa, as revealed by our high-pressure x-ray diffraction studies at room temperature. We tentatively assign the high-pressure modification to an AMo2S4-type phase, a distorted variant of the monoclinic Cr3S4 structure. Furthermore, our Raman investigation provides evidence for a pressure-induced insulator-metal transition. Our density functional theory calculations successfully reproduce the structural transition. They indicate significant band gap and magnetic moment reduction accompanying the pressure-induced structural modification. We discuss our findings in conjunction with the available high-pressure results on other Cr-based chalcogenide spinels.