Generation of photocurrents in semiconducting materials requires dissociation of excitons into free charge carriers. While thermal agitation is sufficient to induce dissociation in most bulk materials, an additional push is required to induce efficient dissociation of the strongly bound excitons in monolayer transition metal dichalcogenides (TMDs). Recently, static in-plane electric fields have proven to be a promising candidate. In the present paper, we introduce a numerical procedure, based on exterior complex scaling, capable of computing field-induced exciton dissociation rates for a wider range of field strengths than previously reported in the literature. We present both Stark shifts and dissociation rates for excitons in various TMDs calculated within the Mott-Wannier model. Here, we find that the field-induced dissociation rate is strongly dependent on the dielectric screening environment. Furthermore, applying weak-field asymptotic theory to the Keldysh potential, we are able to derive an analytical expression for exciton dissociation rates in the weak-field region.