The assembly of individual molecules into hierarchical structures is a promising strategy for developing three-dimensional materials with properties arising from interaction between the individual building blocks. Virus capsids are elegant examples of biomolecular nanostructures, which are themselves hierarchically assembled from a limited number of protein subunits. Here, we demonstrate the bio-inspired modular construction of materials with two levels of hierarchy: the formation of catalytically active individual virus-like particles (VLPs) through directed self-assembly of capsid subunits with enzyme encapsulation, and the assembly of these VLP building blocks into three-dimensional arrays. The structure of the assembled arrays was successfully altered from an amorphous aggregate to an ordered structure, with a face-centered cubic lattice, by modifying the exterior surface of the VLP without changing its overall morphology, to modulate interparticle interactions. The assembly behavior and resultant lattice structure was a consequence of interparticle interaction between exterior surfaces of individual particles and thus independent of the enzyme cargos encapsulated within the VLPs. These superlattice materials, composed of two populations of enzyme-packaged VLP modules, retained the coupled catalytic activity in a two-step reaction for isobutanol synthesis. This study demonstrates a significant step toward the bottom-up fabrication of functional superlattice materials using a self-assembly process across multiple length scales and exhibits properties and function that arise from the interaction between individual building blocks.