Inversion symmetry breaking combined with strong spin-orbit coupling in transition metal dichalcogenides such as MoS2 offers important opportunities for spintronics. We investigate excitons in MoS2 monolayers in an applied in-plane electric field. Tight-binding and Bethe-Salpeter equation calculations predict a large quadratic Stark shift. The scaling of the Stark shifts with the exciton binding energy and the dielectric environment provides a path to engineering the MoS2 electro-optical response. Our results suggest that the excitonic Stark effect can be observed experimentally in a MoS2 monolayer and we explain its implications for spintronic devices.