Abstract: Active matter refers to a collection of individuals, from animal groups to micro-organisms to cytoskeletal filaments, that extract energy from their surroundings at a single-particle level to generate motion and forces. Active matter displays a wide range of emergent behaviors, such as coordinated migration, self-organization, phase transitions, and self-assembly. Here we show that Plasmodium sporozoites, a crescent-shaped form of malaria parasites, provide a unique model system of active matter that combines the aspects of self-propulsion, curved shape, and mechanical flexibility into one system. We investigate the motion of sporozoites in collectives extracted from the salivary glands of mosquitoes, where they form large rotating vortices. We find that single sporozoites within the vortices are sorted according to their curvatures and speeds. Further, the vortices undergo oscillatory breathing in their shape. We explain these intriguing observations using agent-based simulations where each agent is represented by an active curved polymer that mimics the behavior of a motile sporozoite. In summary, we establish malaria parasites as a new active matter system and provide novel insight into the role of shape and mechanics in collective behavior.