We report a three-dimensional (3D) mesoscale heterostructure composed of one-dimensional (1D) nanowire (NW) arrays epitaxially grown on two-dimensional (2D) nanoplates. Specifically, three facile syntheses are developed to assemble vertical ZnO NWs on CuGaO2 (CGO) nanoplates in mild aqueous solution conditions. The key to the successful 3D mesoscale integration is the preferential nucleation and heteroepitaxial growth of ZnO NWs on the CGO nanoplates. Using transmission electron microscopy, heteroepitaxy was found between the basal planes of CGO nanoplates and ZnO NWs, which are their respective (001) crystallographic planes, by the observation of a hexagonal Moiré fringes pattern resulting from the slight mismatch between the c planes of ZnO and CGO. Careful analysis shows that this pattern can be described by a hexagonal supercell with a lattice parameter of almost exactly 11 and 12 times the a lattice constants for ZnO and CGO, respectively. The electrical properties of the individual CGO-ZnO mesoscale heterostructures were measured using a current-sensing atomic force microscopy setup to confirm the rectifying p-n diode behavior expected from the band alignment of p-type CGO and n-type ZnO wide band gap semiconductors. These 3D mesoscale heterostructures represent a new motif in nanoassembly for the integration of nanomaterials into functional devices with potential applications in electronics, photonics, and energy.