Toxoplasma gondii contains an essential plastid organelle called the apicoplast that is necessary for fatty acid, isoprenoid, and heme synthesis. Perturbations affecting apicoplast function or inheritance lead to parasite death. The apicoplast is a single copy organelle and therefore must be divided so that each daughter parasite inherits an apicoplast during cell division. In this study we identify new roles for F-actin and an unconventional myosin motor, TgMyoF, in this process. First, loss of TgMyoF and actin lead to an accumulation of apicoplast vesicles in the cytosol indicating a role for this actomyosin system in apicoplast protein trafficking or morphological integrity of the organelle. Second, live cell imaging reveals that during division the apicoplast is highly dynamic, exhibiting branched, U-shaped and linear morphologies that are dependent on TgMyoF and actin. In parasites where movement was inhibited by the depletion of TgMyoF, the apicoplast fails to associate with the parasite centrosomes. Thus, this study provides crucial new insight into mechanisms controlling apicoplast-centrosome association, a vital step in the apicoplast division cycle, which ensures that each daughter inherits a single apicoplast.