<p>Understanding how atoms collectively interact with light is important for both fundamental studies and the design of light–matter interfaces in quantum technologies. Over the past decades, many experiments have arranged atoms in ordered arrays and used constructive and destructive interference to enhance or suppress coupling to electromagnetic fields, thereby tailoring collective light–matter interactions. These studies have mainly considered one- and two-dimensional arrays. However, only three-dimensional arrays can suppress coherent light scattering in all directions, but such omnidirectional suppression has not been observed experimentally. Here we observe a strong reduction of light scattering in a three-dimensional atomic array prepared as a Mott insulator in optical lattices. The residual scattering arises from the delocalization of atoms, Raman processes and inelastic scattering associated with saturation. We also demonstrate that light scattering can probe density fluctuations in many-body states, allowing us to characterize the superfluid-to-Mott-insulator transition and defects generated during dynamical parameter ramps. These results provide a route to prepare subradiant states for photon storage and to probe correlations in many-body systems in optical lattices.</p>