Recent theoretical predictions and angle-resolved photoemission spectroscopy measurements have shown that single crystal Cd3As2 is a three-dimensional topological Dirac semimetal possessing linear dispersions along all three momentum directions. Nanoscale topological Dirac semimetal structures have a large surface-to-volume ratio and provide a platform to explore its topological surface states. Here we report the synthesis of high quality Cd3As2 single crystalline nanoplates and nano-octahedrons via a vaporsolid growth mechanism. Triangular and hexagonal nanoplates with lateral dimensions ranging from several hundred nanometers to tens of micrometers are obtained. The top facets are (112), consistent with the natural cleavage plane of Cd3As2 single crystal. The synthesized Cd3As2 nano-octahedrons are enclosed by the {112} facets. A photovoltaic effect is demonstrated from a Cd3As2 nanoplate/metal electrode interface, suggesting potential applications in self-powered photodetection.