The discovery of efficient sources of terahertz radiation has been exploited in imaging applications(1), and developing a nanoscale terahertz source could lead to additional applications. High-frequency mechanical vibrations of charged nanostructures can lead to radiative emission, and vibrations at frequencies of hundreds of kilohertz have been observed from a ZnO nanobelt under the influence of an alternating electric field(2). Here, we observe mechanical resonance and radiative emission at similar to 0.36 THz from core-shell ZnO mesocrystal microspheres excited by a continuous green-wavelength laser. We find that similar to 0.016% of the incident power is converted into terahertz radiation, which corresponds to a quantum efficiency of similar to 33%, making the ZnO microspheres competitive with existing terahertz-emitting materials(1,3). The mechanical resonance and radiation stem from the coherent photoinduced vibration of the hexagonal ZnO nanoplates that make up the microsphere shells. The ZnO microspheres are formed by means of a nonclassical, self-organized crystallization process(4-6), and represent a straightforward route to terahertz radiation at the nanoscale.