Stark effect, the electric-field analogue of magnetic Zeeman effect, is one of the celebrated phenomena in modern physics and appealing for emergent applications in electronics, optoelectronics, as well as quantum technologies. While in condensed matter it has prospered only for excitons, whether other collective excitations can display Stark effect remains elusive. Here, we report the observation of phonon Stark effect in a two-dimensional quantum system of bilayer 2H-MoS. The longitudinal acoustic phonon red-shifts linearly with applied electric fields and can be tuned over ~1 THz, evidencing giant Stark effect of phonons. Together with many-body ab initio calculations, we uncover that the observed phonon Stark effect originates fundamentally from the strong coupling between phonons and interlayer excitons (IXs). In addition, IX-mediated electro-phonon intensity modulation up to ~1200% is discovered for infrared-active phonon A. Our results unveil the exotic phonon Stark effect and effective phonon engineering by IX-mediated mechanism, promising for a plethora of exciting many-body physics and potential technological innovations.