Transition metal dichalcogenides such as MoS2 represent promising candidates for building blocks of ultra-thin nanophotonic devices. For such applications, vertically-oriented MoS2 (v-MoS2) nanosheets could be advantageous as compared to conventional horizontal MoS2 (h-MoS2) given that their inherent broken symmetry would favor an enhanced nonlinear response. However, the current lack of a controllable and reproducible fabrication strategy for v-MoS2 limits the exploration of this potential. Here we present a systematic study of the growth of v-MoS2 nanosheets based on the sulfurization of a pre-deposited Mo-metal seed layer. We demonstrate that the sulfurization process at high temperatures is driven by the diffusion of sulfur from the vapor-solid interface to the Mo seed layer. Furthermore, we verify an enhanced nonlinear response in the resulting v-MoS2 nanostructures as compared to their horizontal counterparts. Our results represent a stepping stone towards the fabrication of low-dimensional TMD-based nanostructures for versatile nonlinear nanophotonic devices.