Toxoplasma gondiicontains an essential single plastid organelle known as the apicoplast that is necessary for fatty acid, isoprenoid, and heme synthesis. Perturbations affecting apicoplast function leads to parasite death. To maintain a functional apicoplast, the parasite must execute two important cellular processes: accurate division of this single copy organelle into daughter parasites during cell division and trafficking of nuclear encoded apicoplast proteins (NEAT). In this study we demonstrate that F-actin and an unconventional myosin motor, TgMyoF, are important for both processes. Live cell imaging demonstrates that during division the apicoplast is highly dynamic, exhibiting branched, U-shaped and linear morphologies that are dependent on TgMyoF and actin. These dynamics appear to control apicoplast association with the centrosome and positioning of the centrosome at the apicoplast tips. Loss of apicoplast dynamics correlated with reduced apicoplast-centrosome association and ultimately apicoplast inheritance defects. In addition, we uncovered the role of TgMyoF and actin in NEAT protein trafficking. Vesicles containing the apicoplast protein APT1 were only observed during apicoplast division in control parasites, however loss of TgMyoF and actin lead to accumulation of vesicles in the cytosol, with only a small impact on vesicle movement suggesting that this actomyosin system is important for vesicle fusion with the apicoplast. Consequently, loss of TgMyoF resulted in reduced apicoplast length. This study has provided crucial new insight into mechanisms and timing of protein trafficking to the apicoplast and demonstrated how apicoplast-centrosome association, a key step in the apicoplast division cycle, is control by the actomyosin cytoskeleton.