In computer-aided drug design, the rapid identification of drugs is critical for combating diseases. A key method in this field is molecular docking, which aims to predict the interactions between two molecules. Molecular docking involves long simulations running compute-intensive algorithms, and thus, can profit a lot from hardware-based acceleration. In this work, we investigate the performance efficiency of the SX-Aurora TSUBASA vector computer for such simulations. Specifically, we present our methodology for porting and optimizing AutoDock, a widely-used molecular docking program. Using a number of platform-specific code optimizations, we achieved executions on the SX-Aurora TSUBASA that are in average 3.6× faster than on modern 128-core CPU servers, and up to a certain extent, competitive to V100 and A100 GPUs. To the best of our knowledge, this is the first molecular docking implementation for the SX-Aurora TSUBASA.