During the blood stage of human malaria, Plasmodium falciparum parasites divide by schizogony-a process wherein components for several daughter cells are produced within a common cytoplasm and then segmentation, a synchronized cytokinesis, produces individual invasive daughters. The basal complex is hypothesized to be required for segmentation, acting as a contractile ring to establish daughter cell boundaries. Here we identify an essential component of the basal complex which we name PfCINCH. Using three-dimensional reconstructions of parasites at electron microscopy resolution, we show that while parasite organelles form and divide normally, PfCINCH-deficient parasites develop inviable conjoined daughters that contain components for multiple cells. Through biochemical evaluation of the PfCINCH-containing complex, we discover multiple previously undescribed basal complex proteins. Therefore, this work provides genetic evidence that the basal complex is required for precise segmentation and lays the groundwork for a mechanistic understanding of how the parasite contractile ring drives cell division.