Diffusion processes and local dynamic equilibria inside cells lead to nonuniform spatial distributions of molecules, which are essential for processes such as nuclear organization and signaling in cell division, differentiation and migration. To understand these mechanisms, spatially resolved quantitative measurements of protein abundance, mobilities and interactions are needed, but current methods have limited capabilities to study dynamic parameters. Here we describe a microscope based on light-sheet illumination that allows massively parallel fluorescence correlation spectroscopy (FCS) measurements and use it to visualize the diffusion and interactions of proteins in mammalian cells and in isolated fly tissue. Imaging the mobility of heterochromatin protein HP1α (ref. 4) in cell nuclei we could provide high-resolution diffusion maps that reveal euchromatin areas with heterochromatin-like HP1α-chromatin interactions. We expect that FCS imaging will become a useful method for the precise characterization of cellular reaction-diffusion processes.