Abstract: The Stark effect is one of the most efficient mechanisms to manipulate many-body states in nanostructured systems. In mono- and few-layer transition metal dichalcogenides, it has been successfully induced by optical and electric field means. Here, we tune the optical emission energies and dissociate excitonic states in MoSe2 monolayers employing the 220 MHz in-plane piezoelectric field carried by surface acoustic waves. We transfer the monolayers to high dielectric constant piezoelectric substrates, where the neutral exciton binding energy is reduced, allowing us to efficiently quench (above 90%) and red-shift the excitonic optical emissions. A model for the acoustically induced Stark effect yields neutral exciton and trion in-plane polarizabilities of 530 and 630 x 10(-5) meV/(kV/cm)(2), respectively, which are considerably larger than those reported for monolayers encapsulated in hexagonal boron nitride. Large in-plane polarizabilities are an attractive ingredient to manipulate and modulate multiexciton interactions in two-dimensional semiconductor nanostructures for optoelectronic applications.