The final step during cell division is the separation of daughter cells, a process that requires the coordinated delivery and assembly of new membrane to the cleavage furrow. While most eukaryotic cells replicate by binary fission, replication of apicomplexan parasites involves the assembly of daughters (merozoites/tachyzoites) within the mother cell, using the so-called Inner Membrane Complex (IMC) as a scaffold. After de novo synthesis of the IMC and biogenesis or segregation of new organelles, daughters bud out of the mother cell to invade new host cells. Here, we demonstrate that the final step in parasite cell division involves delivery of new plasma membrane to the daughter cells, in a process requiring functional Rab11A. Importantly, Rab11A can be found in association with Myosin-Tail-Interacting-Protein (MTIP), also known as Myosin Light Chain 1 (MLC1), a member of a 4-protein motor complex called the glideosome that is known to be crucial for parasite invasion of host cells. Ablation of Rab11A function results in daughter parasites having an incompletely formed IMC that leads to a block at a late stage of cell division. A similar defect is observed upon inducible expression of a myosin A tail-only mutant. We propose a model where Rab11A-mediated vesicular traffic driven by an MTIP-Myosin motor is necessary for IMC maturation and to deliver new plasma membrane to daughter cells in order to complete cell division.