Alarming environmental changes and the threat of natural fuel resource extinction are concerning issues in human development. This has increased scientists’ efforts to phase out traditional energy resources and move on to environmentally friendly biofuels. In this study, non-edible castor oil was transesterified with methanol using a manganese-doped zinc oxide (Mn-doped ZnO) nanocatalyst. A heterogeneous nanocatalyst was prepared by means of the the sonochemical method. X-ray diffraction (XRD), energy dispersive X-ray spectroscopy (EDX), and transmission electron microscopy (TEM) were used to characterize these nanocatalysts. The transesterification reaction was studied under different temperature conditions, different ratios of methyl alcohol to castor oil, and different amounts of the catalyst to identify optimum conditions in which the maximum yield of biodiesel was produced. The maximum biodiesel yield (90.3%) was observed at 55 °C with an oil-to-methanol ratio of 1:12, and with 1.2 g of nanocatalyst. The first-order kinetic model was found to be the most suitable. Several thermodynamic parameters were also determined, such as activation energy, enthalpy, and entropy. We found that this transesterification was an endergonic and entropy-driven reaction. The results showed that the Mn-doped ZnO nanocatalyst could be a suitable catalyst for the heterogeneous catalytic transesterification process, which is essential for biodiesel production.