Motility is a fundamental part of cellular life and survival, including for Plasmodium parasites--single-celled protozoan pathogens responsible for human malaria. The motile life cycle forms achieve motility, called gliding, via the activity of an internal actomyosin motor. Although gliding is based on the well-studied system of actin and myosin, its core biomechanics are not completely understood. Currently accepted models suggest it results from a specifically organized cellular motor that produces a rearward directional force. When linked to surface-bound adhesins, this force is passaged to the cell posterior, propelling the parasite forwards. Gliding motility is observed in all three life cycle stages of Plasmodium: sporozoites, merozoites and ookinetes. However, it is only the ookinetes--formed inside the midgut of infected mosquitoes--that display continuous gliding without the necessity of host cell entry. This makes them ideal candidates for invasion-free biomechanical analysis. Here we apply a plate-based imaging approach to study ookinete motion in three-dimensional (3D) space to understand Plasmodium cell motility and how movement facilitates midgut colonization. Using single-cell tracking and numerical analysis of parasite motion in 3D, our analysis demonstrates that ookinetes move with a conserved left-handed helical trajectory. Investigation of cell morphology suggests this trajectory may be based on the ookinete subpellicular cytoskeleton, with complementary whole and subcellular electron microscopy showing that, like their motion paths, ookinetes share a conserved left-handed corkscrew shape and underlying twisted microtubular architecture. Through comparisons of 3D movement between wild-type ookinetes and a cytoskeleton-knockout mutant we demonstrate that perturbation of cell shape changes motion from helical to broadly linear. Therefore, while the precise linkages between cellular architecture and actomyosin motor organization remain unknown, our analysis suggests that the molecular basis of cell shape may, in addition to motor force, be a key adaptive strategy for malaria parasite dissemination and, as such, transmission.