Parallelized fluorescence imaging has been a long-standing pursuit that can address the unmet need for a comprehensive three-dimensional (3D) visualization of dynamical biological processes with minimal photodamage. However, the available approaches are limited to incomplete parallelization in only two dimensions or sparse sampling in three dimensions. We hereby develop a novel fluorescence imaging approach, called coded light-sheet array microscopy (CLAM), which allows complete parallelized 3D imaging without mechanical scanning. Harnessing the concept of an "infinity mirror", CLAM generates a light-sheet array with controllable sheet density and degree of coherence. Thus, CLAM circumvents the common complications of multiple coherent light-sheet generation in terms of dedicated wavefront engineering and mechanical dithering/scanning. Moreover, the encoding of multiplexed optical sections in CLAM allows the synchronous capture of all sectioned images within the imaged volume. We demonstrate the utility of CLAM in different imaging scenarios, including a light-scattering medium, an optically cleared tissue, and microparticles in fluidic flow. CLAM can maximize the signal-to-noise ratio and the spatial duty cycle, and also provides a further reduction in photobleaching compared to the major scanning-based 3D imaging systems. The flexible implementation of CLAM regarding both hardware and software ensures compatibility with any light-sheet imaging modality and could thus be instrumental in a multitude of areas in biological research.